A lifting theorem for symmetric commutants

Author:
Gelu Popescu

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1705-1711

MSC (2000):
Primary 47F25, 47A57, 47A20; Secondary 30E05

DOI:
https://doi.org/10.1090/S0002-9939-00-05750-6

Published electronically:
October 31, 2000

MathSciNet review:
1814100

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be bounded operators on a Hilbert space such that . Given a symmetry on , i.e., , we define the -symmetric commutant of to be the operator space

In this paper we obtain lifting theorems for symmetric commutants. The result extends the Sz.-Nagy-Foias commutant lifting theorem (), the anticommutant lifting theorem of Sebestyén ( ), and the noncommutative commutant lifting theorem ( ). Sarason's interpolation theorem for is extended to symmetric commutants on Fock spaces.

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Additional Information

**Gelu Popescu**

Affiliation:
Division of Mathematics and Statistics, The University of Texas at San Antonio, San Antonio, Texas 78249

Email:
gpopescu@math.utsa.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05750-6

Received by editor(s):
March 1, 1999

Received by editor(s) in revised form:
September 16, 1999

Published electronically:
October 31, 2000

Additional Notes:
The author was partially supported by NSF Grant DMS-9531954.

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society