Spaceability in Banach and quasi-Banach sequence spaces

Abstract

Let $X$ be a Banach space. We prove that, for a large class of Banach or quasi-Banach spaces $E$ of $X$-valued sequences, the sets $E-{\bigcup }_{q\in \Gamma }{\ell }_q(X)$, where $\Gamma$ is any subset of $(0,\infty ]$, and $E-c_0(X)$ contain closed infinite-dimensional subspaces of $E$ (if non-empty, of course). This result is applied in several particular cases and it is also shown that the same technique can be used to improve a result on the existence of spaces formed by norm-attaining linear operators.

9 pages

References in corpus (1)

• A note on lineability