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

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6 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	115-118
Nombre de pages	4
journal	Monatshefte fur Mathematik
Volume	164
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s00605-010-0216-x
état	Publié - 1 sept. 2011
Modification externe	Oui

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10.1007/s00605-010-0216-x

Contient cette citation

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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.",

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KW - Convolution operators on groups

KW - Inverse-closed subalgebras of B(H)

KW - Schur algebra

KW - Symmetric Banach algebras

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

Résumé

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Contient cette citation

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