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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 189–202 (Mi mz8040)  

This article is cited in 1 scientific paper (total in 1 paper)

Geometric characterization of $RN$-operators

O. I. Reinov

Institute of Social and Economical Problems, Academy of Sciences of the USSR

Abstract: Let $X$ and $Y$ be Banach spaces and $T\in L(X,Y)$. An operator $T:X\to Y$ is called an $RN$-operator if it transforms every $X$-valued. measure $\overline m$ of bounded variation into a $Y$-valued measure having a derivative with respect to the variation of the measure $\overline m$. The notions of $T$-dentability and $Ts$-dentability of bounded sets in Banach spaces are introduced and in their terms are given conditions equivalent to the condition that $T$ is an $RN$-operator (Theorem 1). It is also proved that the adjoint operator is an $RN$-operator if and only if for every separable subspace $X_0$ of $X$ the set $(T|X_0)^*(Y^*)$ is separable (Theorem 2).

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English version:
Mathematical Notes, 1977, 22:2, 597–604

Bibliographic databases:

UDC: 513.8
Received: 23.12.1975

Citation: O. I. Reinov, “Geometric characterization of $RN$-operators”, Mat. Zametki, 22:2 (1977), 189–202; Math. Notes, 22:2 (1977), 597–604

Citation in format AMSBIB
\Bibitem{Rei77}
\by O.~I.~Reinov
\paper Geometric characterization of $RN$-operators
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 189--202
\mathnet{http://mi.mathnet.ru/mz8040}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=500278}
\zmath{https://zbmath.org/?q=an:0371.47031}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 597--604
\crossref{https://doi.org/10.1007/BF01780967}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. I. Reinov, “Purely topological characteristics of operators of type $RN$”, Funct. Anal. Appl., 12:4 (1978), 317–319  mathnet  crossref  mathscinet  zmath
  • Математические заметки Mathematical Notes
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