Embedding $\ell_{\infty}$ into the space of all Operators on Certain Banach Spaces

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dc.creatorAndroulakis, G.
dc.creatorBeanland, K.
dc.creatorDilworth, S. J.
dc.creatorSanacory, F.
dc.date2004-12-08
dc.date.accessioned2026-07-07T05:15:06Z
dc.date.available2026-07-07T05:15:06Z
dc.descriptionWe give sufficient conditions on a Banach space $X$ which ensure that $\ell_{\infty}$ embeds in $\mathcal{L}(X)$, the space of all operators on $X$. We say that a basic sequence $(e_n)$ is quasisubsymmetric if for any two increasing sequences $(k_n)$ and $(\ell_n)$ of positive integers with $k_n \leq \ell_n$ for all $n$, we have that $(e_{k_n})$ dominates $(e_{\ell_n})$. We prove that if a Banach space $X$ has a seminormalized quasisubsymmetric basis then $\ell_{\infty}$ embeds in $\mathcal{L}(X)$.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0412171
dc.identifierhttp://arxiv.org/abs/math/0412171
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73526
dc.subjectFunctional Analysis
dc.subject46B28; 46B03
dc.titleEmbedding $\ell_{\infty}$ into the space of all Operators on Certain Banach Spaces
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