Abstract of a paper by Fernando Albiac, Jose L. Ansorena, Przemyslaw Wojtaszczyk
This is an announcement for the paper “On a 'philosophical' question about Banach envelopes” by Fernando Albiac<https://arxiv.org/search/math?searchtype=author&query=Albiac%2C+F>, Jose L. Ansorena<https://arxiv.org/search/math?searchtype=author&query=Ansorena%2C+J+L>, Przemyslaw Wojtaszczyk<https://arxiv.org/search/math?searchtype=author&query=Wojtaszczyk%2C+P>. Abstract: We show how to construct nonlocally convex quasi-Banach spaces $X$ whose dual separates the points of a dense subspace of $X$ but does not separate the points of $X$. Our examples connect with a question raised by Pietsch [About the Banach envelope of $l_{1,\infty}$, Rev. Mat. Complut. 22 (2009), 209-226] and shed light into the unexplored class of quasi-Banach spaces with nontrivial dual which do not have sufficiently many functionals to separate the points of the space. https://arxiv.org/abs/2003.07742
participants (1)
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Bentuo Zheng (bzheng)