caa a22 4500 445868678 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00605-010-0216-x doi (NATIONALLICENCE)springer-10.1007/s00605-010-0216-x Tessera Romain CNRS, ENS de Lyon, 46, Allée d'Italie, 69364, Lyon Cedex 07, France aut The inclusion of the Schur algebra in B ( ℓ 2) is not inverse-closed [Elektronische Daten] [Romain Tessera] The Schur algebra is the algebra of operators which are bounded on ℓ 1 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 ℓ 2, and whose inverse is not bounded on ℓ 1 nor on ℓ ∞. In particular, this shows that the Schur algebra is not inverse-closed. Springer-Verlag, 2010 Inverse-closed subalgebras of B(H) nationallicence Symmetric Banach algebras nationallicence Schur algebra nationallicence Convolution operators on groups nationallicence Monatshefte für Mathematik Springer Vienna 164/1(2011-09-01), 115-118 0026-9255 164:1<115 2011 164 605 https://doi.org/10.1007/s00605-010-0216-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0216-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tessera Romain CNRS, ENS de Lyon, 46, Allée d'Italie, 69364, Lyon Cedex 07, France aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/1(2011-09-01), 115-118 0026-9255 164:1<115 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer