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Mat. Zametki, 1978, Volume 23, Issue 2, Pages 305–314 (Mi mz8145)  

Universal measurability of the identity mapping of a Banach space in certain topologies

V. I. Rybakov

Tula State Pedagogical Institute

Abstract: If $X$ is a Banach space and $X'$ is its conjugate, then a subset $Y$ of $X'$ is called madmissible for $X$ if a) he topology $\sigma(X,Y)$ is Hausdorff, b) the identity embedding of ($X,\sigma(X,Y)$) into $X$ is universally measurable (Ref. Zh. Mat., 1975, 8B 75 8K). If $X$ is separable, then the existence of an $m$-admissible set is well known. In this note it is shown that there exist nonseparable $X$ having separable $m$-admissible sets. The properties of spaces with separable $m$-admissible sets are considered. It is proved, in particular, that a separable normalizing subset $Y$ of $X'$ is $m$-admissible for $X$ if and only if every $\sigma(X,Y)$-compact set is separable in $X$.

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English version:
Mathematical Notes, 1978, 23:2, 164–168

Bibliographic databases:

UDC: 513.8
Received: 09.05.1976

Citation: V. I. Rybakov, “Universal measurability of the identity mapping of a Banach space in certain topologies”, Mat. Zametki, 23:2 (1978), 305–314; Math. Notes, 23:2 (1978), 164–168

Citation in format AMSBIB
\Bibitem{Ryb78}
\by V.~I.~Rybakov
\paper Universal measurability of the identity mapping of a~Banach space in certain topologies
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 2
\pages 305--314
\mathnet{http://mi.mathnet.ru/mz8145}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=493275}
\zmath{https://zbmath.org/?q=an:0404.46010}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 2
\pages 164--168
\crossref{https://doi.org/10.1007/BF01153161}


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