Hilbert modules over a class of semicrossed products

Author:
Dale R. Buske

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1721-1726

MSC (2000):
Primary 47H20, 46M18; Secondary 47A15, 47A45, 47A56

Published electronically:
November 2, 2000

MathSciNet review:
1814102

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Given the disk algebra and an automorphism , there is associated a non-self-adjoint operator algebra called the semicrossed product of with . Buske and Peters showed that there is a one-to-one correspondence between the contractive Hilbert modules over and pairs of contractions and on satisfying . In this paper, we show that the orthogonally projective and Shilov Hilbert modules over correspond to pairs of isometries on satisfying . The problem of commutant lifting for is left open, but some related results are presented.

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Additional Information

**Dale R. Buske**

Affiliation:
Department of Mathematics, St. Cloud State University, St. Cloud, Minnesota 56301

Email:
dbuske@stcloudstate.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05691-4

Keywords:
Commutant lifting,
Hilbert modules,
Shilov modules,
orthogonally projective modules

Received by editor(s):
June 23, 1998

Received by editor(s) in revised form:
September 17, 1999

Published electronically:
November 2, 2000

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society