Hereditarily Indecomposable Banach algebras of diagonal operators

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dc.creatorArgyros, Spiros A.
dc.creatorDeliyanni, Irene
dc.creatorTolias, Andreas G.
dc.date2009-02-10
dc.date.accessioned2026-07-07T12:39:52Z
dc.date.available2026-07-07T12:39:52Z
dc.descriptionWe provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with respect to $(e_n)_{n\in\mathbb{N}}$ . We also construct a Hereditarily Indecomposable Banach space ${\mathfrak X}_D$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ such that ${\mathfrak X}^*_D$ is isometric to $\mathcal{L}_{diag}({\mathfrak X}_D)$ with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every $T\in \mathcal{L}_{diag}({\mathfrak X}_D)$ is of the form $T=λI+K$, where $K$ is a compact operator.
dc.description35 pages, submitted for publication to Israel J. Math
dc.identifierhttps://arxiv.org/abs/0902.1646
dc.identifierhttp://arxiv.org/abs/0902.1646
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219271
dc.subjectFunctional Analysis
dc.subject46B28, 47L10, 46B20, 46B03.
dc.titleHereditarily Indecomposable Banach algebras of diagonal operators
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