On spectrality of the algebra of convolution dominated operators

Gero Fendle, Karlheinz Gröchenig, and Michael Leinert. "On spectrality of the algebra of convolution dominated operators." Banach Center Publications 78.1 (2007): 145-149. <http://eudml.org/doc/282285>.

@article{GeroFendle2007,
abstract = {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].},
author = {Gero Fendle, Karlheinz Gröchenig, Michael Leinert},
journal = {Banach Center Publications},
keywords = {convolution dominated operators; inverse-closed subalgebras; symmetry},
language = {eng},
number = {1},
pages = {145-149},
title = {On spectrality of the algebra of convolution dominated operators},
url = {http://eudml.org/doc/282285},
volume = {78},
year = {2007},
}

TY - JOUR
AU - Gero Fendle
AU - Karlheinz Gröchenig
AU - Michael Leinert
TI - On spectrality of the algebra of convolution dominated operators
JO - Banach Center Publications
PY - 2007
VL - 78
IS - 1
SP - 145
EP - 149
AB - 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].
LA - eng
KW - convolution dominated operators; inverse-closed subalgebras; symmetry
UR - http://eudml.org/doc/282285
ER -