An extremely non-homogeneous weak Hilbert space

Argyros, Spiros; Beanland, Kevin; Raikoftsalis, Theocharis

doi:10.1090/S0002-9947-2012-05592-9

An extremely non-homogeneous weak Hilbert space
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by Spiros A. Argyros, Kevin Beanland and Theocharis Raikoftsalis PDF

Trans. Amer. Math. Soc. 364 (2012), 4987-5014 Request permission

Abstract:

We construct a weak Hilbert Banach space such that for every block subspace $Y$ every bounded linear operator on $Y$ is of the form $D+S$, where $S$ is a strictly singular operator and $D$ is a diagonal operator. We show that this yields a weak Hilbert space whose block subspaces are not isomorphic to any of their proper subspaces.

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