Strictly singular non-compact diagonal operators on HI spaces

Details Strictly singular non-compact diagonal operators on HI spaces Strictly singular non-compact diagonal operators on HI spaces

2008-07-15

arxiv.org/abs/0807.2388v1

Mathematics

Functional Analysis

Scientific paper

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
$\ell_{\infty}(\N)$.

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