Transactions of the American Mathematical Society

Symmetry and inverse-closedness of matrix algebras and functional calculus for infinite matrices

Author(s): Karlheinz Gröchenig; Michael Leinert
Journal: Trans. Amer. Math. Soc. 358 (2006), 2695-2711.
MSC (2000): Primary 47B37, 47A60, 46H30, 42C15
Posted: January 24, 2006
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Abstract: We investigate the symbolic calculus for a large class of matrix algebras that are defined by the off-diagonal decay of infinite matrices. Applications are given to the symmetry of some highly non-commutative Banach algebras, to the analysis of twisted convolution, and to the theory of localized frames.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 47B37, 47A60, 46H30, 42C15

Karlheinz Gröchenig
Affiliation: Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269-3009
Address at time of publication: Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria
Email: groch@math.uconn.edu, karlheinz.groechenig@univie.ac.at

Michael Leinert
Affiliation: Fakultät für Mathematik, Institut für Angewandte Mathematik, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
Email: leinert@math.uni-heidelberg.de

DOI: 10.1090/S0002-9947-06-03841-4
PII: S 0002-9947(06)03841-4
Keywords: Off-diagonal decay of matrices, weight function, invertibility of operators, invariance of spectrum, symmetric Banach algebras, Gelfand-Raikov-Shilov condition, Schur's test, twisted convolution, localized frames
Received by editor(s): November 4, 2003
Received by editor(s) in revised form: August 13, 2004
Posted: January 24, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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