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The Measure Algebra of the Heisenberg Group

✍ Scribed by L.A. Coburn

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 149 KB
Volume: 161
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3354

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✦ Synopsis

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 , the C*-algebra generated by [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 .

1999 Academic Press z } a=z 1 aÄ 1 +z 2 aÄ 2 + } } } +z n aÄ n for aÄ j the complex conjugate of a j , and |z| 2 =z } z. The Heisenberg group H n is given by H n =C n _R with multiplication (a, t)(b, s)=(a+b, s+t+Im b } aÂ2),

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