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arXiv · 0910.3285

The inclusion of the Schur algebra in B(l^2) is not inverse-closed

Romain Tessera
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Abstract

The Schur algebra is the algebra of operators which are bounded on l^1 and on l^{\infty}. Q. Sun conjectured that the Schur algebra is inverse-closed. In this note, we disprove this conjecture. Precisely, we exhibit an operator in the Schur algebra, invertible in l^2, whose inverse is not bounded on l^1 nor on l^{\infty}.

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Romain Tessera. 2009-10-17. The inclusion of the Schur algebra in B(l^2) is not inverse-closed. https://arxiv.org/abs/0910.3285

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