The Measure Algebra of the Heisenberg Group

L. A. Coburn

doi:10.1006/jfan.1998.3354

The Measure Algebra of the Heisenberg Group

L. A. Coburn

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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 p, the C*-algebra generated by p[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 ℂⁿ.

Original language	English
Pages (from-to)	509-525
Number of pages	17
Journal	Journal of Functional Analysis
Volume	161
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1998.3354
State	Published - Feb 1 1999

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title = "The Measure Algebra of the Heisenberg Group",

abstract = "Irreducible representations of the convolution algebra M(ℍn) of bounded regular complex Borel measures on the Heisenberg group ℍn are analyzed. For the Segal-Bargmann representation p, the C*-algebra generated by p[M(ℍn)] 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 ℂn.",

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N2 - Irreducible representations of the convolution algebra M(ℍn) of bounded regular complex Borel measures on the Heisenberg group ℍn are analyzed. For the Segal-Bargmann representation p, the C*-algebra generated by p[M(ℍn)] 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 ℂn.

AB - Irreducible representations of the convolution algebra M(ℍn) of bounded regular complex Borel measures on the Heisenberg group ℍn are analyzed. For the Segal-Bargmann representation p, the C*-algebra generated by p[M(ℍn)] 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 ℂn.

UR - https://www.scopus.com/pages/publications/0010982389

U2 - 10.1006/jfan.1998.3354

DO - 10.1006/jfan.1998.3354

M3 - Article

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SN - 0022-1236

VL - 161

SP - 509

EP - 525

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

The Measure Algebra of the Heisenberg Group

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