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


Authors: Karlheinz Gröchenig and Michael Leinert
Journal: Trans. Amer. Math. Soc. 358 (2006), 2695-2711
MSC (2000): Primary 47B37, 47A60, 46H30, 42C15
DOI: https://doi.org/10.1090/S0002-9947-06-03841-4
Published electronically: January 24, 2006
MathSciNet review: 2204052
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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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Additional Information

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: https://doi.org/10.1090/S0002-9947-06-03841-4
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
Published electronically: January 24, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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