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On spectrality of the algebra of convolution dominated operators

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Fendle G., Gröchenig K., Leinert M.

Banach Center Publications

2007

tom 78

nr 1

145-149

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].

Ograniczanie wyników

1 Banach Center Publications

1 Fendle G.

1 Gröchenig K.

1 Leinert M.

1 2007

Wyniki wyszukiwania

On spectrality of the algebra of convolution dominated operators