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

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

2009-10-17

arxiv.org/abs/0910.3285v1

Mathematics

Functional Analysis

3 pages

Scientific paper

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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