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A CHARACTERIZATION OF SUBSPACES OF WEAKLY COMPACTLY GENERATED BANACH SPACES

  • M. FABIAN (a1), V. MONTESINOS (a2) and V. ZIZLER (a3)

Abstract

It is proved that a Banach space $X$ is a subspace of a weakly compactly generated Banach space if and only if, for every $\varepsilon\,{>}\,0$, $X$ can be covered by a countable collection of bounded closed convex symmetric sets where the weak$^*$ closure in $X^{**}$ of each of them lies within the distance $\varepsilon$ from $X$. A new short functional-analytic proof of the known result that a continuous image of an Eberlein compact is Eberlein is given as a corollary.

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A CHARACTERIZATION OF SUBSPACES OF WEAKLY COMPACTLY GENERATED BANACH SPACES

  • M. FABIAN (a1), V. MONTESINOS (a2) and V. ZIZLER (a3)

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