Spaceability in Banach and quasi-Banach sequence spaces

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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-∪ q∈Γℓq(X), where Γ is any subset of (0,∞], and E-c0(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. © 2010 Elsevier Inc. All rights reserved.

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Botelho, G., Diniz, D., Fávaro, V. V., & Pellegrino, D. (2011). Spaceability in Banach and quasi-Banach sequence spaces. Linear Algebra and Its Applications, 434(5), 1255–1260. https://doi.org/10.1016/j.laa.2010.11.012

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