Geodesic
From history of one unpublished paper of M.~I.~Kadets
Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 307-319.

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Authors of paper put before themselves a problem: to acquaint the mathematical public with unpublished paper of the outstanding Soviet mathematician M.I.Kadets heading the Kharkov school, known for the works in the field of the theory of Banach spaces, to tell story of this paper. The given work continues paper of the author about part cooperation and interaction of teachers and scientists of the Tula state pedagogical university of L.N.Tolstoy and Michael Iosifovich Kadetsa's Kharkov school. Under its management the Tula student which afterwards after training at Michael Iosifovich Kadetsa's Kharkov school became the candidate of physical and mathematical sciences conducted scientific work. Michael Iosifovich by right is considered one of founders of the theory of equivalent renormings of the Banach spaces, turned now in independent area. The Kharkov school Kadetsa has at that time become world-famous. M.I.Kadets generously shared the mathematical ideas with the pupils. In paper some joint outcomes received by M.I.Kadetsem and its pupil in 1988-1990 which prepared for the publication in the form of joint paper but then have not been published because of high insistence which was shown to itself by outstanding Soviet mathematician M. I. Kadets, to insistence which can be an example for modern youth, especially for scientific youth are reduced. The study was carried out at the expense of budgetary funds according to the state assignment of the Financial University No. 15841p-P8.
Keywords: history of mathematics, functional analysis, Banach spaces, Tula mathematics, mathematicians of the Mikhail Iosifovich Kadets Kharkiv School. 
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E. V. Manokhin; R. A. Zhukov; I. V. Bormotov; I. V. Dobrynina; Е. A. Nazirova. From history of one unpublished paper of M.~I.~Kadets. Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 307-319. http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a23/

[1] Manokhin, E. V., Kozlova, N. O., Komov, V. E., “Kharkiv school of M. I. Kadets and mathematics of Tula”, Chebyshevskii sbornik, 22:4 (2021), 323–330 | DOI | MR

[2] Manokhin, E. V., Ustyan, A. E., Kuznetsov, G. V., “Scholar and teacher. To the 80-th anniversary of Vladislav Ivanovich Rybakov (13.12.1939–27.09.2016)”, Chebyshevskii sbornik, 20:4 (2019), 450–457 | DOI | MR | Zbl

[3] Rybakov, V. I., “On conditional mathematical expectations for functions integrable in the Pettis sense”, Math. Notes, 10:5 (1971), 764–767 | DOI | MR | Zbl

[4] Rybakov, V. I., “Vector measures with values in locally convex spaces”, Funct. Anal. Appl., 7:4 (1973), 339–340 | DOI | MR

[5] Rybakov, V. I., “The separation from a vector measure of the part representable by a Bochner integral”, Math. Notes, 17:5 (1975), 476–482 | DOI | MR | Zbl

[6] Rybakov, V. I., “A generalization of the Bochner integral to locally convex spaces”, Math. Notes, 18:4 (1975), 933–938 | DOI | MR | MR | Zbl

[7] Rybakov, V. I., “Certain cases of the reduction of the study of weakly integrable functions to the study of Pettis-integrable functions”, Soviet Math. (Iz. VUZ), 19:11 (1975), 84–86 | MR | Zbl

[8] V. I. Rybakov, “K teoreme Bartla–Danforda–Shvartsa o vektornykh merakh”, Matem. zametki, 7:2 (1970), 247–254 | MR

[9] W. J. Ricker, “Rybakov s theorem in Frechet spaces and completeness of L1-spaces”, Austral. Math. Soc. (Series A), 64 (1998), 247–252 | DOI | MR | Zbl

[10] A. Fernandez and F. Naranjo, “Rybakov's theorem for vector measures in Frechet spaces”, Indag. Math. (NewSeries), 8 (1997), 33–42 | DOI | MR | Zbl

[11] Lyubich, Yu. I., Marchenko, V. A., Novikov, S. P., Ostrovskii, M. I., Pastur, L. A., Plichko, A. N., Popov, M. M., Semenov, E. M., Troyanskii, S. L., Fonf V. P., Khruslov, E. Ya., “Mikhail Iosifovich Kadets (obituary)”, Russian Math. Surveys, 66:4 (2011), 809–811 | DOI | DOI | MR | Zbl

[12] Kadets M. I., “Topological equivalence of all separable Banach spaces”, Dokl. Akad. Nauk SSSR, 167 (1966), 23–25 (Russian) | Zbl

[13] Kadets, M. I., “Proof of the topological equivalence of all separable infinite-dimensional Banach spaces”, Funct. Anal. Appl., 1:1 (1967), 61–70 | Zbl

[14] Milvutin A. A., “Isomorphism of spaces of continuous functions over compact sets of continuum cardinality”, The Function theory, a functional analysis and their applications, 2 (1966), 150–156 (Russian) | Zbl

[15] Kadets M. I, “Topological equivalence of all separable Banach spaces”, Dokl. Akad. Nauk SSSR, 167 (1966), 23–25 (Russian) | Zbl

[16] Clarkson J.A., “Uniformly convex spaces”, Trans. Amer. Math. Soc., 40:3 (1936), 396–414 | DOI | MR | Zbl

[17] Lovaglia A.R., “Locally uniformly convex Banach spaces”, Trans. Amer. Math. Soc., 78:1 (1955), 225–238 | DOI | MR | Zbl

[18] Kadets M. I., “Spaces isomorphic to a locally uniformly convex space”, Izv. Vvssh. Uchebn. Zaved. Mat., 6 (1959), 51–57 (Russian) | Zbl

[19] Lindenstrauss J., “Weakly compacts sets-their topological properties and Banach spaces they generate”, Ann. Math. Studies, 69 (1972), 235–273 | MR | Zbl

[20] Trojanski S.L., “About equivalent norms and the minimum systems in nonseparable Banach spaces”, The Function theory, Funkts. analysis and their applications, 43 (1972), 125–138 (Russian) | Zbl

[21] Kadets M. I., “About connection between weak and a strong convergence”, DAN UkrSSRAM, 1959, 949–952 (Russian)

[22] Beazamv V., Introduction to Banach Spaces and their Geometry, Oxford, 1985, 334 pp. | MR

[23] Deville R., Godefrov G., Zizler V., Smoothness and renorming in Banach spaces, Pitman monographs and surveys in pure and applied mathematics, 64, Longman scientific and technical, Longman house, Burnt mill, Harrow, 1993 | MR

[24] Aleksandrov P. S., Introduction in the theory of sets and the general topology, The Science, M., 1977

[25] Havdon R.G., “Trees in renorming theory”, Proc. London Math. Soc., 78 (1999), 541–584 | DOI | MR

[26] Havdon R.G., Zizler V., “A new spaces with no locally uniformly rotund renorming”, Can. Math. Bull., 32:1 (1989), 122–128 | DOI | MR

[27] Havdon R.G., Hajek P., “Smooth norms and approximation in Banach spaces of the type S(K)”, The Quarterly Journal of Mathematics, 58 (2007), 221–228 | DOI | MR

[28] Havdon R.G., “Locally uniformly convex norms in Banach spaces and their duals”, J. Funct. Anal., 254:8 (2008), 2023–2039 | DOI | MR

[29] Havdon R.G., Argvros S.A., “A hereditarily indecomposable L-infinitv-space that solves the scalar-plus-compact problem”, Acta Mathematica, 206:1 (2011), 1–54 | DOI | MR

[30] Bormotov I., The valuable world of modern Russian youth (The social-philosophical analysis), the monography, Infra-M, M., 2022