Abstract of a paper by Romain Tessera
This is an announcement for the paper "The inclusion of the Schur algebra in B(l^2) is not inverse-closed" by Romain Tessera. 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}. Archive classification: math.FA math.MG Mathematics Subject Classification: 47B38, 47B37 Remarks: 3 pages The source file(s), Schuralgebra.tex: 6835 bytes, is(are) stored in gzipped form as 0910.3285.gz with size 3kb. The corresponding postcript file has gzipped size 44kb. Submitted from: tessera@phare.normalesup.org The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.3285 or http://arXiv.org/abs/0910.3285 or by email in unzipped form by transmitting an empty message with subject line uget 0910.3285 or in gzipped form by using subject line get 0910.3285 to: math@arXiv.org.
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alspach@fourier.math.okstate.edu