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Gero Fendler Karlheinz Gröchenig Michael Leinert 《Integral Equations and Operator Theory》2008,61(4):493-509
We study infinite matrices A indexed by a discrete group G that are dominated by a convolution operator in the sense that for x ∈ G and some . This class of “convolution-dominated” matrices forms a Banach-*-algebra contained in the algebra of bounded operators on
ℓ
2(G). Our main result shows that the inverse of a convolution-dominated matrix is again convolution-dominated, provided that
G is amenable and rigidly symmetric. For abelian groups this result goes back to Gohberg, Baskakov, and others, for non-abelian
groups completely different techniques are required, such as generalized L
1-algebras and the symmetry of group algebras.
K. G. was supported by the Marie-Curie Excellence Grant MEXT-CT 2004-517154. 相似文献
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M.?Isabel?Garridomontalvo@unex.es" title="igarrido@unex.es montalvo@unex.es" itemprop="email" data-track="click" data-track-action="Email author" data-track-label="">Email author Francisco?Montalvo 《Positivity》2005,9(1):81-95
For a linear sublattice of C(X), the set of all real continuous functions on the completely regular space X, we denote by A() the smallest uniformly closed and inverse-closed subalgebra of C(X) that contains . In this paper we study different methods to generate A() from . For that, we introduce some families of functions which are defined in terms of suprema or sums of certain countably many functions in . And we prove that A() is the uniform closure of each of these families. We obtain, in particular, a generalization of a known result about the generation of A() when is a uniformly closed linear sublattice of bounded functions. 相似文献
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