Properties of bounded and precompact by measure sets

A.A. Korniienko (Dnipropetrovsk State University)
S.A. Pichugov (Dnipropetrovsk State University), https://orcid.org/0000-0002-4263-4429

Abstract


In the space of convergence by measure we investigate the properties of convex bounded and convex precompact sets.

References


Berg J., Lofstrom J. Interpolative spaces, 1980. (in Russian)

Krasnoselskii M.A., Zabreiko P.P., Pustylnik Ye.I., Sobolevskii P.Ye. Integral operators in spaces of summable functions, 1966. (in Russian)

Nikishin Ye.M. "Resonance theorems and superlinear operators", Uspekhi matem. nauk, 1970; 25(6): pp. 129-191. (in Russian) doi:10.1070/RM1970v025n06ABEH001270

Pichugov S.A. "Sequences of operators that are bounded in measure", Matem. sbornik, 1994; 185(1): pp. 43-72. (in Russian) doi:10.1070/SM1995v081n01ABEH003613

Rudin W. Functional Analysis, 1975. (in Russian)

Maurey B. "Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces $$$L^p$$$", Asterisque, 1974; 11: pp. 1-163. (in French)

Pichugov S.A. "Translation invariant operators in linear metric spaces", Analysis Math., 1992; 18(3): pp. 237-248. doi:10.1007/bf01911088

Stein E.M. "On limits of sequences of operators", Ann. Math., 1961; 74(1): pp. 140-170. doi:10.2307/1970308




DOI: https://doi.org/10.15421/249809

  

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Copyright (c) 1998 A.A. Korniienko, S.A. Pichugov

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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