Toeplitz algebras and Rieffel deformations

L. A. Coburn; Jingbo Xia

doi:10.1007/BF02099582

Toeplitz algebras and Rieffel deformations

Mathematics

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9 Scopus citations

Abstract

We establish a representation theorem for Toeplitz operators on the Segal-Bargmann (Fock) space of Cⁿ whose "symbols" have uniform radial limits. As an application of this result, we show that Toeplitz algebras on the open ball in Cⁿ are "strict deformation quantizations", in the sense of M. Rieffel, of the continuous functions on the corresponding closed ball.

Original language	English
Pages (from-to)	23-38
Number of pages	16
Journal	Communications in Mathematical Physics
Volume	168
Issue number	1
DOIs	https://doi.org/10.1007/BF02099582
State	Published - Mar 1995

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title = "Toeplitz algebras and Rieffel deformations",

abstract = "We establish a representation theorem for Toeplitz operators on the Segal-Bargmann (Fock) space of Cn whose {"}symbols{"} have uniform radial limits. As an application of this result, we show that Toeplitz algebras on the open ball in Cn are {"}strict deformation quantizations{"}, in the sense of M. Rieffel, of the continuous functions on the corresponding closed ball.",

author = "Coburn, \{L. A.\} and Jingbo Xia",

year = "1995",

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T1 - Toeplitz algebras and Rieffel deformations

AU - Coburn, L. A.

AU - Xia, Jingbo

PY - 1995/3

Y1 - 1995/3

N2 - We establish a representation theorem for Toeplitz operators on the Segal-Bargmann (Fock) space of Cn whose "symbols" have uniform radial limits. As an application of this result, we show that Toeplitz algebras on the open ball in Cn are "strict deformation quantizations", in the sense of M. Rieffel, of the continuous functions on the corresponding closed ball.

AB - We establish a representation theorem for Toeplitz operators on the Segal-Bargmann (Fock) space of Cn whose "symbols" have uniform radial limits. As an application of this result, we show that Toeplitz algebras on the open ball in Cn are "strict deformation quantizations", in the sense of M. Rieffel, of the continuous functions on the corresponding closed ball.

UR - https://www.scopus.com/pages/publications/21844492140

U2 - 10.1007/BF02099582

DO - 10.1007/BF02099582

M3 - Article

AN - SCOPUS:21844492140

SN - 0010-3616

VL - 168

SP - 23

EP - 38

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -

Toeplitz algebras and Rieffel deformations

Abstract

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