On spectrality of the algebra of convolution dominated operators

• Autorzy: Gero Fendle , Karlheinz Gröchenig , Michael Leinert
• Języki publikacji: EN

Abstrakty

EN

If G is a discrete group, the algebra CD(G) of convolution dominated operators on l²(G) (see Definition 1 below) is canonically isomorphic to a twisted L¹-algebra $l¹(G,l^{∞}(G),T)$. For amenable and rigidly symmetric G we use this to show that any element of this algebra is invertible in the algebra itself if and only if it is invertible as a bounded operator on l²(G), i.e. CD(G) is spectral in the algebra of all bounded operators. For G commutative, this result is known (see [1], [6]), for G noncommutative discrete it appears to be new. This note is about work in progress. Complete details and more will be given in [3].

Kategorie tematyczne

• 43A20: L 1 -algebras on groups, semigroups, etc.
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 78
• Numer: 1
• Strony: 145-149

Daty

wydano

2007

Twórcy

autor

Gero Fendle

• Finstertal 16, D-69514 Laudenbach, Germany

autor

Karlheinz Gröchenig

• Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria

autor

Michael Leinert

• Institut für Angewandte Mathematik, Fakultät für Mathematik, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany

Identyfikatory

DOI

10.4064/bc78-0-10