A weak Hilbert space with few symmetries

Mathematics – Functional Analysis

Scientific paper

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32 pages

Scientific paper

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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