The inclusion of the Schur algebra in B(ℓ2) is not inverse-closed

Romain Tessera

doi:10.1007/s00605-010-0216-x

The inclusion of the Schur algebra in B(ℓ²) is not inverse-closed

Romain Tessera

Ecole Normale Supérieure de Lyon

Research output: Contribution to journal › Article › peer-review

Abstract

The Schur algebra is the algebra of operators which are bounded on ℓ¹ and on ℓ^∞. In this note, we exhibit an element of the group algebra of the free group with two generators, which, as a convolution operator, is invertible in ℓ², and whose inverse is not bounded on ℓ¹ nor on ℓ^∞. In particular, this shows that the Schur algebra is not inverse-closed.

Original language	English
Pages (from-to)	115-118
Number of pages	4
Journal	Monatshefte fur Mathematik
Volume	164
Issue number	1
DOIs	https://doi.org/10.1007/s00605-010-0216-x
Publication status	Published - 1 Sept 2011
Externally published	Yes

Keywords

Convolution operators on groups
Inverse-closed subalgebras of B(H)
Schur algebra
Symmetric Banach algebras

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10.1007/s00605-010-0216-x

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KW - Symmetric Banach algebras

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The inclusion of the Schur algebra in B(ℓ²) is not inverse-closed

Abstract

Keywords

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