[Banach] Abstract of a paper by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias

This is an announcement for the paper "Strictly singular non-compact diagonal operators on HI spaces" by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias.

Abstract: We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with respect to the basis \seq{e}{n} contains an isomorphic copy of $\ell_{\infty}(\N)$. \end{abstract}

Archive classification: math.FA

Mathematics Subject Classification: 46B28, 46B20, 46B03

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Submitted from: sargyros@math.ntua.gr

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