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Spaceability in Banach and quasi-Banach sequence spaces. (English) Zbl 1226.46017

Summary: 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.

MSC:

46B45 Banach sequence spaces
46A45 Sequence spaces (including Köthe sequence spaces)
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
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