Mikhail M. Popov

Professor of Mathematics

Books and book chapters

2. M. Popov. Rademacher type independence in Boolean algebrasIn the book: The Mathematical Legacy of Victor Lomonosov. Operator Theory. De Gruyter, Berlin-Boston (2020), 327-348. DOI: https://doi.org/10.1515/9783110656756 

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

82. A. Gumenchuk, I. Krasikova, M. Popov. On linear sections of orthogonally additive operatorsSubmitted (2022).

81. V. MykhaylyukM. Popov. $\varepsilon$-shading operator on Riesz spaces and order continuity of orthogonally additive operatorsSubmitted (2022).

80. O. Fotiy, A. GumenchukM. Popov. More on the extension of linear operators on Riesz spacesSubmitted (2021).

79. V. Mykhaylyuk, M. Pliev, M. Popov. The lateral order on Riesz spaces and orthogonally additive operators. IISubmitted (2021).

78. O. Fotiy, I. Krasikova, M. Pliev, M. Popov. Order continuity of orthogonally additive operatorsResults in Math. 77, no 5 (2022) published online https://link.springer.com/article/10.1007%2Fs00025-021-01543-x 

77. N. Dzhusoeva, M.S. Moslehian, M. Pliev, M. Popov. Operators taking values in Lebesgue-Bochner spacesSubmitted (2021).

76. M. Pliev, M. Popov. Representation theorems for regular linear and orthogonally additive operatorsSubmitted (2020).

75. M. Popov. Banach lattices of orthogonally additive operatorsJ. Math. Anal. Appl. (2022) - published online 29 April 2022, 126279. DOI: https://doi.org/10.1016/j.jmaa.2022.126279 

74. I. Krasikova, M. Pliev, M. Popov. Measurable Riesz spacesCarpathian 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 spacesProc. 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 retractsCarpathian 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 spaceCarpathian 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)-spacesCarpathian 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: 10.1016/j.jmaa.2019.123487

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: 10.1007/s11117-019-00666-4

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: 10.1155/2019/8569409

64. O. Maslyuchenko, M. Popov. More on representation of operators on L1. J. Math. Anal. Appl. 470 (2) (2019), 679–689. MR3870583, DOI: https://doi.org/10.1016/j.jmaa.2018.05.083

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: https://doi.org/10.1007/s11117-017-0497-6

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: https://doi.org/10.1134/S0037446616030198

59. V. Mykhaylyuk, M. Pliev, M. Popov, O. Sobchuk. Dividing measures and narrow operators, Stud. Math. 231 (2) (2015), p. 97–116. MR3465282, DOI: 10.4064/sm7878-2-2016

58. A. Gumenchuk, O. Karlova, M. Popov. Order Schauder bases in Banach lattices, J. Funct. Anal. 269 (2) (2015), p. 536–550. MR3348826, DOI: https://doi.org/10.1016/j.jfa.2015.04.008

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: https://doi.org/10.1007/s11856-014-0012-8

56. M. Pliev, M. Popov. Narrow orthogonally additive operators, Positivity 18 (4) (2014), 641–667. MR3275358, DOI: https://doi.org/10.1007/s11117-013-0268-y

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: http://dx.doi.org/10.12988/ijma.2014.44118

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: https://doi.org/10.2478/s11533-013-0358-x

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: https://doi.org/10.1016/j.jmaa.2013.03.008

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: https://doi.org/10.1016/j.jfa.2011.03.007

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: 10.4064/bc92-0-21

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: https://doi.org/10.1007/s00013-010-0105-5

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: https://doi.org/10.1007/s11117-008-2193-z

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: https://doi.org/10.1007/s11253-006-0050-4

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 lsubspace 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 Land 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