Maximal spaceability in sequence spaces (Q454839)

A set \(A\) in a topological vector space \(E\) is said to be maximally spaceable if \(A \cup\{ 0\} \) contains a subspace of the dimension of \(E\). The authors show that for several classical sequence spaces, if a certain set of sequences is non-empty, then for any infinite-dimensional Banach space \(X\), the corresponding set of \(X\)-valued sequences is maximally spaceable. The fairly general approach the authors take allows to conclude, for example, that the sets \(c_0(X)-\bigcup_{p>0} \ell^w_p(X)\), \(\ell^p(X)-\bigcup_{0<q<p}\ell^w_q(X)\) are maximally spaceable.