Books and book chapters
3. M. Pliev, M. Popov. Orthogonally additive operators on vector lattices. In: Aron, R.M., Moslehian, M.S., Spitkovsky, I.M., Woerdeman, H.J. (eds) Operator and Norm Inequalities and Related Topics. Trends in Mathematics. Birkhäuser, Cham, 2022, pp.321-351. https://doi.org/10.1007/978-3-031-02104-6_10
2. M. Popov. Rademacher-type independence in Boolean algebras. The Mathematical Legacy of Victor Lomonosov: Operator Theory, edited by Richard M. Aron, Eva A. Gallardo Gutiérrez, Miguel Martin, Dmitry Ryabogin, Ilya M. Spitkovsky and Artem Zvavitch, Berlin, Boston: De Gruyter, 2020, pp. 327-348. https://doi.org/10.1515/9783110656756-021
1. M. Popov, B. Randrianantoanina, Narrow Operators on Function Spaces and Vector Lattices, De Gruyter Studies in Mathematics 45, De Gruyter, Berlin-Boston, 2013. MR2985035 DOI: https://doi.org/10.1515/9783110263343
Scientific Papers
84. M. Popov. A note on narrow operators on complex Riesz spaces. Proc. Amer. Math. Soc. Published electronically: February 2, 2024. DOI: https://doi.org/10.1090/proc/16660
83. M. Pliev, M. Popov. Representation theorems for regular linear and orthogonally additive operators. Math. Nachr. 297, no 1 (2024), 126–143. https://doi.org/10.1002/mana.202200129
82. V. Mykhaylyuk, M. Pliev, M. Popov. The lateral order on Riesz spaces and orthogonally additive operators. II. Positivity 28, 8 (2024). https://doi.org/10.1007/s11117-023-01025-0
81. O. Fotiy, V. Kadets, M. Popov. Some remarks on orthogonally additive operators on Riesz spaces. Positivity 27, 57 (2023). https://doi.org/10.1007/s11117-023-01008-1
80. N. Dzhusoeva, M.S. Moslehian, M. Pliev, M. Popov. Operators, taking values in Lebesgue-Bochner spaces. Proc. Amer. Math. Soc. 151, no 8 (2023), 3493-3502. DOI: https://doi.org/10.1090/proc/16350 https://www.ams.org/journals/proc/2023-151-08/S0002-9939-2023-16350-9/?active=current
79. A. Gumenchuk, I. Krasikova, M. Popov. On linear sections of orthogonally additive operators. Mat. Stud. 58, no 1 (2022), 94-102. DOI: https://doi.org/10.30970/ms.58.1.94-102
78. V. Mykhaylyuk, M. Popov. $\varepsilon$-shading operator on Riesz spaces and order continuity of orthogonally additive operators. Results in Math. 77, 209 (2022). https://doi.org/10.1007/s00025-022-01742-0
77. O. Fotiy, A. Gumenchuk, M. Popov. More on the extension of linear operators on Riesz spaces. Carpathian Math. Publ. 14, no 2 (2022), 327-331. DOI: https://doi.org/10.15330/cmp.14.2.327-331
76. O. Fotiy, I. Krasikova, M. Pliev, M. Popov. Order continuity of orthogonally additive operators. Results in Math. 77, no 1 (2022), Paper No. 5, 19 pp. https://link.springer.com/article/10.1007%2Fs00025-021-01543-x
75. M. Popov. Banach lattices of orthogonally additive operators. J. Math. Anal. Appl. 514, no 1 (2022), Paper No. 126279, 26 pp. DOI: https://doi.org/10.1016/j.jmaa.2022.126279
74. I. Krasikova, M. Pliev, M. Popov. Measurable Riesz spaces. Carpathian Math. Publ. 13, no 1 (2021), 81-88. DOI: https://doi.org/10.15330/cmp.13.1.81-88
73. M. Popov. Horizontal Egorov property of Riesz spaces. Proc. Amer. Math. Soc. 149, no 1 (2021), 323-332. DOI: https://doi.org/10.1090/proc/15235
72. V. Mykhaylyuk, M. Pliev, M. Popov. The lateral order on Riesz spaces and orthogonally additive operators. Positivity 25, no 2 (2021), 291-327. DOI: https://doi.org/10.1007/s11117-020-00761-x
71. I.V. Krasikova, M.A. Pliev, M.M. Popov, O.G. Fotiy. On separate order continuity of orthogonally additive operators (dedicated to the memory of V.K. Maslyuchenko). Bukovinian Math. J. 9, no 1 (2021) (in Ukrainian). DOI: https://doi.org/10.31861/bmj2021.01.17
70. A. Kamińska, I. Krasikova, M. Popov. Projection lateral bands and lateral retracts. Carpathian Math. Publ. 12, no 2 (2020), 333-339. DOI: https://doi.org/10.15330/cmp.12.2.333-339
69. O. Fotiy, M. Ostrovskii, M. Popov. Isomorphic spectrum and isomorphic length of a Banach space. Carpathian Math. Publ. 12, no 1 (2020), 88-93. https://doi.org/10.15330/cmp.12.1.88-93
68. M. Popov. On two long standing open problems on Lp(µ)-spaces. Carpathian Math. Publ. 12, no 1 (2020), 229-241. https://doi.org/10.15330/cmp.12.1.229-241
67. V. Mykhaylyuk, M. Popov. On geometric entropy in Hilbert spaces. J. Math. Anal. Appl. 481, no 2 (2020). MR4008015, DOI:
66. O. Fotiy, A. Gumenchuk, I. Krasikova, M. Popov. On sums of narrow and compact operators. Positivity. 24, no 1 (2020), 69–80. MR4052682, DOI:
65. O. Maslyuchenko, M. Popov. On sums of strictly narrow operators acting from a Riesz space to a Banach space. J. Funct. Spaces. (2019), Art. ID 8569409, 6 pp.. MR3963605, DOI:
64. O. Maslyuchenko, M. Popov. More on representation of operators on L1. J. Math. Anal. Appl. 470 (2) (2019), 679–689. MR3870583, DOI:
63. M. M. Popov, O. V. Sobchuk. On the “function” and “lattice” definitions of a narrow operator, Positivity. 22 (1) (2018), 59–62. MR3764630, DOI:
62. A. I. Gumenchuk, M. M. Popov. On the sum of a narrow and a finite rank operators on vector lattices, Bukovinian Math. J. 5 (1-2) (2017), 62–70 (in Ukrainian). http://bmj.fmi.org.ua/index.php/adm/article/view/232
61. A. I. Gumenchuk, I. V. Krasikova, M. M. Popov. Points of narrowness and uniformly narrow operators, Carpathian Math. Publ. 9 (1) (2017), 37–47. MR3669975, DOI: 10.15330/cmp.9.1.37-47
60. M. Pliev, M. Popov. On extension of abstract Uryson operators, Sib. Mat. Zh. 57 (3) (2016), p. 700–708 (in Russian). MR3548797, DOI:
59. V. Mykhaylyuk, M. Pliev, M. Popov, O. Sobchuk. Dividing measures and narrow operators, Stud. Math. 231 (2) (2015), p. 97–116. MR3465282, DOI:
58. A. Gumenchuk, O. Karlova, M. Popov. Order Schauder bases in Banach lattices, J. Funct. Anal. 269 (2) (2015), p. 536–550. MR3348826, DOI:
57. V. Mykhaylyuk, M. Popov, B. Randrianantoanina, G. Schechtman. Narrow and l2-strictly singular operators from Lp, Israel J. Math. 203 (1) (2014), p. 81–108. MR3273433, DOI:
56. M. Pliev, M. Popov. Narrow orthogonally additive operators, Positivity 18 (4) (2014), 641–667. MR3275358, DOI:
55. A. Dorogovtsev, M. Popov. Geometric entropy in Banach spaces, Theory Stoch. Process. 19 (2) (2014), 10–30. MR3405380, http://tsp.imath.kiev.ua/files/1920/art1920_02.pdf
54. M. Pliev M., M. Popov. Dominated Uryson operators, Int. J. Math. Anal. (Ruse) 8 (22) (2014), 1051–1059. DOI:
53. M. Pliev, M. Popov, O. Sobchuk. Up-martingales in vector lattices, Int. J. Math. Anal. (Ruse) 8 (22) (2014), 1041–1050. DOI: http://dx.doi.org/10.12988/ijma.2014.44117
52. M. Popov, E. Semenov, D. Vatsek. Some problems on narrow operators on function spaces, Cent. Eur. J. Math. 12 (3) (2014), 476–482. MR3145905, DOI:
51. M. Popov, D. Vatsek. Wide operators on Köthe function spaces, Mat. Stud. 42 (1) (2014), 104–112. MR3381394, http://matstud.org.ua/texts/2014/42_1/104-112.html
50. A. Gumenchuk, M. Pliev, M. Popov, Extensions of orthogonally additive operators, Mat. Stud. 41 (2) (2014), 214–219. MR3289104, http://matstud.org.ua/texts/2014/41_2/214-219.html
49. I. V. Krasikova, M. M. Popov, An application of Kadets-Pełczyński sets to narrow operators, Zh. Mat. Fiz. Anal. Geom. 9 (1) (2013), 102–107. MR3097549, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=jmag&paperid=551&option_lang=eng
48. V. Mykhaylyuk, M. Popov, On sums of narrow operators on Köthe function spaces. J. Math. Anal. Appl. 404 (2) (2013), 554–561. MR3045194, DOI:
47. I. Krasikova and M. Popov, A note on operators from Köthe function spaces to c0(Γ), Carpathian Math. Publ. 4 (1) (2012), 67–71 (in Ukrainian). http://journals.pu.if.ua/index.php/cmp/article/view/87
46. A. M. Plichko, M. M. Popov, Some open problems on Banach spaces, Mat. Stud. 38 (2) (2012), 203–211. MR3058486, http://matstud.org.ua/texts/2012/38_2/203-211.html
45. V. Kholomenyuk, V. Mykhaylyuk and M. Popov, On isomorphisms of some Köthe function F-spaces, Central European J. Math. 9 (6) (2011), 1267–1275. MR2836719 (2012g:46008)
44. M. Martín, J. Merí and M. Popov, On the numerical radius of operators in Lebesgue spaces, J. Funct. Anal. 261 (1) (2011), 149–168. MR2785896, DOI:
43. M. Martín, J. Merí and M. Popov, On the numerical index of the real Lp(µ)-spaces, Israel J. Math. 184 (2011), 183–192. MR2823974 (2012g:46032). DOI: 10.1007/S11856-011-0064-Y
42. M. Popov, Narrow operators (a survey), Function spaces IX Banach Center Publ., Inst. of Math. Polish Acad. Sci., Warszawa, 92 (2011), 299–326. MR2884464, DOI:
41. M. Martin, J. Meri, M. Popov and B. Randrianantoanina, Numerical index of absolute sums of Banach spaces, J. Math. Anal. Appl. 375 (1) (2011), p. 207–222. MR2735706 (2011j:46017) DOI: 10.1016/J.JMAA.2010.08.061
40. M. Martín, J. Merí and M. Popov, The polynomial Daugavet property for atomless L1(µ)-spaces, Arch. Math. (Basel) 94 (4) (2010), 383–389. MR2643972, DOI:
39. I. V. Krasikova and M. M. Popov, On a generalization of the notion of compact operator on the spaces Lp, Nauk. Visn. Chernivetskoho Univ., Mat. (Chernivtsi), 501 (2010), p. 38–42 (in Ukrainian). Zbl 1240.46058
38. I. V. Krasikova, V. V. Mykhaylyuk and M. M. Popov, Operators defined on L1 which «nowhere» attain their norm, Methods Funct. Anal. Topology 16 (1) (2010), 17–27. MR 2656128 (2011d: 46024)
37. O. V. Maslyuchenko, V. V. Mykhaylyuk and M. M. Popov, A lattice approach to narrow operators, Positivity, 13 (3) (2009), p. 459–495. MR2511237, DOI:
36. A. A. Dorogovtsev and M. M. Popov, On narrowness of conditional expectation operators in spaces of measurable functions, Mat. Visn. Nauk. Tov. Im. Shevchenka, 5, (1) (2008), p. 36–46 (in Ukrainian). Zbl 1199.46075
35. M. M. Popov, An exact Daugavet type inequality for small into isomorphi- sms in L1, Arch. Math. (Basel), 90, No 6 (2008) p. 537–544. MR 2415297, DOI: https://doi.org/10.1007/s00013-008-2559-2
34. O. V. Maslyuchenko, V. V. Mykhaylyuk and M. M. Popov, Asymptotic structure and the existence of noncompact operators between Banach spaces, J. Funct. Anal., 253 (2) (2007), p. 550–560. MR 2370089 https://doi.org/10.1016/j.jfa.2007.08.015
33. M. M. Popov, Complemented subspaces and some problems of the modern geometry of Banach spaces, Mat. Siohodni, 13 (2007), p. 78–116 (in Ukrainian). MR 2541898 (2010h: 46017)
32. V. V. Mykhaylyuk and M. M. Popov, Weak embeddings of L1, Houston J. Math., 32 (4) (2006), p. 1139–1152. MR2268476, https://www.math.uh.edu/~hjm/Vol32-4.html
31. V. V. Mykhaylyuk and M. M. Popov, Some geometric aspects of operators acting from L1, Positivity, 10 (3) (2006), p. 431–466. MR2258952, https://doi.org/10.1007/s11117-005-0041-y
30. O. V. Maslyuchenko, V. V. Mykhaylyuk and M. M. Popov, Theorems on decomposition of operators in L1 and their generalization to vector lattices, Ukr. Mat. Zh., 58 (1) (2006), p. 26–35 (in Ukrainian). English translation: Ukrainian Math. J. 58 (1) (2006), 26–35. MR2244903, DOI:
29. M. M. Popov, The Rosenthal subsequence splitting lemma in L1, Mat. Visn. Nauk. Tov. Im. Shevchenka, 2 (2005), p. 147–150 (in Ukrainian). Zbl 1144.46306
28. A. Martínez-Abejón, E. Odell, M. M. Popov, Some open problems on the classical function space L1, Mat. Stud., 24 (2) (2005), p. 173–191. MR2224004, http://matstud.org.ua/texts/2005/24_2/24_2_173_191.pdf
27. M. M. Popov, A property of convex basic sequences in L1, Methods Funct. Anal. Topology, 11 (4) (2005), p. 409–416. MR2243294, http://mfat.imath.kiev.ua/article/?id=323
26. O. V. Maslyuchenko, V. V. Mykhaylyuk and M. M. Popov, Asymptotic norm and compact operators, Nauk. Visn. Chernivets’koho Univ., Mat. (Cherni- vtsi), 269 (2005), p. 73–75 (in Ukrainian). Zbl 1100.47502, http://bmj.fmi.org.ua/index.php/adm/article/view/485
25. M. M. Popov, Weak embeddings of L1, In: «Some Open Problems on Functional Analysis and Function Theory», eds. V. K. Maslyuchenko and A. M. Plichko, Extracta Math., 20 (1) (2005), p. 66–67. Zbl 1092.46500, https://www.eweb.unex.es/eweb/extracta/Vol-20-1/20J1Masly.pdf
24. M. M. Popov, More examples of hereditarily lp Banach spaces, Ukr. Math. Bull., 2(1) (2005), p. 95–111. MR2172327 (2006h:46010)
23. M. M. Popov, A hereditarily l1 subspace of L1 without the Schur property, Proc. Amer. Math. Soc., 133 (7) (2005), p. 2023–2028. MR2137868, https://www.ams.org/journals/proc/2005-133-07/S0002-9939-05-07758-0/
22. M. M. Popov, Sign-embeddings of the spaces Lp for 0 < p < 1, Nauk. Visn. Chernivets’koho Univ., Mat. (Chernivtsi), 228 (2004), p. 108–109 (in Ukrainian). Zbl 1069.47500, http://bmj.fmi.org.ua/index.php/adm/article/view/451
21. M. M. Popov, Daugavet type inequalities for narrow operators in the space L1, Mat. Stud., 20 (1) (2003), p. 75–84. MR2019599 (2004i:46019), http://matstud.org.ua/texts/2003/20_1/75_84.pdf
20. V. M. Kadets and M. M. Popov, Some stability theorems on narrow operators acting in L1 and C(K), Mat. Fizika, Analiz, Geom., 10 (1) (2003), p. 49–60. MR1937046, https://jmage.ilt.kharkov.ua/main.php?page=10
19. M. M. Popov, Reproducibility of sequences in Banach spaces, Nauk. Visn. Chernivets’koho Univ., Mat. (Chernivtsi), 160 (2003), p. 104–108 (in Ukraini- an). Zbl 1071.46020, http://bmj.fmi.org.ua/index.php/adm/article/view/401
18. M. M. Popov and B. Randrianantoanina, A pseudo-Daugavet property for narrow projections in Lorenz spaces, Ill. J. Math., 46 (4) (2002), p. 1313–1338. MR1988266, https://projecteuclid.org/euclid.ijm/1258138482
17. M. M. Popov, On curves with values in F-spaces, Nauk. Visn. Chernivetskoho Univ., Mat. (Chernivtsi), 76 (2000), p. 92–95 (in Ukrainian). Zbl 1039.26010, http://bmj.fmi.org.ua/index.php/adm/article/view/315
16. V. K. Maslyuchenko, V. V. Mykhaylyuk and M. M. Popov, Partitions of a segment into similar parts, Nauk. Visn. Chernivets’koho Univ., Mat. (Chernivtsi), 46 (1999), p. 88–94 (in Ukrainian). Zbl 1039.26002, http://bmj.fmi.org.ua/index.php/adm/article/view/284
15. V. M. Kadets and M. M. Popov, The Daugavet property for narrow operators in rich subspaces of C[0,1] and L1[0,1], Algebra i Analiz, 8 (4) (1996), p. 43–62 (in Russian). English translation: Petersburg Math. J. 8 (1997), 571– 584. MR1418254, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=aa&paperid=728&option_lang=eng
14. M. M. Popov, On integrability in F-spaces, Stud. Math., 110 (3) (1994), p. 205–220. MR1292843, https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/110/3/108433/on-integrability-in-f-spaces DOI: 10.4064/sm-110-3-205-220
13. V. M. Kadets and M. M. Popov, On the Liapunov convexity theorem with applications to sign-embeddings, Ukr. Mat. Zh., 44 (9) (1992), p. 1192–1200. MR1211141
12. A. N. Plichko and M. M. Popov, Symmetric function spaces on atomless probability spaces, Dissertationes Mathematicae, 306 (1990), p. 1–85. MR1082412 http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.zamlynska-536d8afd-fad6-4cef-b63c-d2829aea1ffd
11. M. M. Popov, An elementary proof of the absence of nonzero compact operators defined on the space Lp, 0 < p < 1, Mat. Zametki, 47 (5) (1990), p. 154–155 (in Russian). MR1068071, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=3251&option_lang=eng
10. V. M. Kadets, A. N. Plichko and M. M. Popov, Complete minimal systems of a certain type in Banach spaces, Izv. Vuzov. Mat., 5 (1988), p. 33– 40 (in Russian). English translation: J. Soviet Math. (Iz. VUZ), 32 (5) (1988), p. 39–48. MR0960964, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=7958&option_lang=eng
9. M. M. Popov, Norms of projections in Lp(µ) with «small» kernels, Funkts. Analiz i Prilozhen., 21 (2) (1987), p. 86–87 (in Russian). English translation: J. Soviet Math., 21 (2) (1987), p. 162–163. MR0902304, https://link.springer.com/article/10.1007%2FBF01078037#citeas
8. M. M. Popov, Isomorphic classification of the spaces Lp for 0 < p < 1, Teor. Funkts., Funkts. Anal. Primenen. (Kharkov), 47 (1987), p. 77–85 (in Russi- an). English translation: J. Soviet Math., 48 (6) (1990), p. 674–681. MR0916446, http://rave.ohiolink.edu/ejournals/article/330666385 DOI: 10.1007/BF01094722
7. V. M. Kadets and M. M. Popov, Schauder bases which are conditional at each hyperoctant, Sibirsk. Mat. Zh., 28 (1) (1987), p. 115–118 (in Russian). Engli- sh translation: Sib. Math. J., 28 (1) (1987), p. 86–89. MR0886859
6. A. N. Plichko and M. M. Popov, Bases in nonseparable symmetric spaces and spaces of almost periodic functions, Izv. Vuzov. Mat., 4 (1987), p. 50–59 (in Russian). MR0904981 (89e:46034), http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=ivm&paperid=7729&option_lang=eng
5. V. K. Maslyuchenko and M. M. Popov, An invariant of partially ordered sets, Mat. Zametki, 38 (6) (1985), p. 866–871 (in Russian). English translation: Math. Notes, 38 (6) (1985), p. 981–984. MR0823424, http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mzm&paperid=5599&option_lang=eng
4. M. M. Popov, Codimension of subspaces of Lp(µ) for p < 1, Funkts. Analiz i Prilozhen., 18 (2) (1984), p. 94–95 (in Russian). English translation: Funct. Anal. Appl., 18 (2) (1984), p. 168–170. MR0745720, https://link.springer.com/article/10.1007%2FBF01077844
3. L. N. Gurvitz, V. K. Maslyuchenko and M. M. Popov, Ordinal characteristics of partially ordered sets, VINITI Report, Chernovtsy State Univ., (1983), 25 p. (in Russian).
2. N. Kurganetsky, M. Bzovy, M. Popov, V. Savulyak and A. Lopushanskaya, Determination of optimal conditions for obtaining crystals with uniform distribution of an admixture, Fizicheskaya Khimiya (Moscow), 57 (1) (1983), p. 38–42 (in Russian).
1. M. M. Popov, Logical connectives as derivatives of the rules of inference, Semiotika i Informatika (Moscow), 21 (1983), p. 89–107 (in Russian). MR0724439
This email address is being protected from spambots. You need JavaScript enabled to view it.Anniversary articles and obituaries
9. Mikhail Ostrovskii (for his 60th birthday) 13 (1) (2021), 272–283. Carpathian Math. Publ. https://journals.pnu.edu.ua/index.php/cmp/article/view/5118/5576
8. Yo. V. Ostrovskii (April 6. 1934 - November 29, 2020), Mat. Studii. 54 (2) (2020), 222–224. http://matstud.org.ua/ojs/index.php/matstud/article/view/166
7. Maslyuchenko Volodymyr (September 26. 1950 - September 25, 2020), Mat. Studii. 54 (1) (2020), 111–112. http://matstud.org.ua/ojs/index.php/matstud/article/view/134
6. Vladimir Mikhailovich Kadets (to 60th anniversary), Visnyk of V.N. Karazin Nat. Univ. Ser. Math., Appl. Math. and Mech. 92 (2020), 57–58. http://vestnik-math.univer.kharkov.ua/Visnyk-KhNU-92-2020-Kadets.pdf
5. Anatolij Mykolajovych Plichko (on the 70-th anniversary), Mat. Visn. Nauk. Tov. Im. Shevchenka 16 (2019), 1–25 (in Ukrainian).
4. Mikhail Iosipfovich Kadets, Russian Math. Surveys 66 (4) (2011), 179–180.
3. To the 60-th anniversary of V.K.Maslyuchenko, Mat. Visn. Nauk. Tov. Im. Shevchenka 7 (2010), 455–483 (in Ukrainian). http://journals.iapmm.lviv.ua/ojs/index.php/MBSSS/article/view/169
2. Anatolij Mykolajovych Plichko (on the 60-th anniversary), Mat. Visn. Nauk. Tov. Im. Shevchenka 6 (2009), 294–312 (in Ukrainian). Zbl 1199.01049
1. Mikhail Iosiphovich Kadets (to 80-th birthday ann.), Uspekhi Mat. Nauk, 59 (5) (2004), p. 183–185 (in Russian). English translation: Russian Math. Surveys 59 (2004), no. 5, p. 1001–1004 MR2125945, DOI: https://doi.org/10.4213/rm790