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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 $X$.

Full text: PDF file (971 kB)

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

Bibliographic databases:

UDC: 513.8

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}