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On spectrality of the algebra of convolution dominated operators

Gero FendleKarlheinz GröchenigMichael Leinert — 2007

Banach Center Publications

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 l ¹ ( 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...

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