Non-Archimedean $K$-spaces
Volume 68 / 2005
Banach Center Publications 68 (2005), 87-93
MSC: Primary 46S10.
DOI: 10.4064/bc68-0-10
Abstract
We study Banach spaces over a non-spherically complete non-Archimedean valued field $K$. We prove that a non-Archimedean Banach space over $K$ which contains a linearly homeomorphic copy of $l^{\infty }$ (hence $l^{\infty }$ itself) is not a $K$-space. We discuss the three-space problem for a few properties of non-Archimedean Banach spaces.
