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The Measure Algebra of the Heisenberg Group

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
161
Issue
2
Identifiers
DOI: 10.1006/jfan.1998.3354
Disciplines
  • Mathematics

Abstract

Abstract Irreducible representations of the convolution algebra M( H n ) of bounded regular complex Borel measures on the Heisenberg group H n are analyzed. For the Segal–Bargmann representation ρ, the C*-algebra generated by ρ[ M( H n )] is just the C*-algebra generated by Berezin–Toeplitz operators with positive-definite “symbols.” This algebra is a deformation of the sup norm algebra generated by positive-definite functions on complex n-space C n .

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