On a 'philosophical' question about Banach envelopes
Functional Analysis
2020-03-18 v1
Abstract
We show how to construct nonlocally convex quasi-Banach spaces whose dual separates the points of a dense subspace of but does not separate the points of . Our examples connect with a question raised by Pietsch [About the Banach envelope of , 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.
Cite
@article{arxiv.2003.07742,
title = {On a 'philosophical' question about Banach envelopes},
author = {Fernando Albiac and Jose L. Ansorena and Przemyslaw Wojtaszczyk},
journal= {arXiv preprint arXiv:2003.07742},
year = {2020}
}