# On spectrality of the algebra of convolution dominated operators

Gero Fendle; Karlheinz Gröchenig; Michael Leinert

Banach Center Publications (2007)

- Volume: 78, Issue: 1, page 145-149
- ISSN: 0137-6934

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topGero 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 -

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