Triangular Toeplitz contractions and Cowen sets for analytic polynomials

Authors:
Muneo Cho, Raúl E. Curto and Woo Young Lee

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3597-3604

MSC (2000):
Primary 47B35, 15A57, 15A60; Secondary 47B20, 30D50

DOI:
https://doi.org/10.1090/S0002-9939-02-06628-5

Published electronically:
May 8, 2002

MathSciNet review:
1920039

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the collection of lower triangular Toeplitz matrices and let be the collection of lower triangular Toeplitz contractions. We show that is compact and strictly convex, in the spectral norm, with respect to ; that is, is compact, convex and , where and denote the topological boundary with respect to and the set of extreme points, respectively. As an application, we show that the reduced Cowen set for an analytic polynomial is strictly convex; more precisely, if is an analytic polynomial and if , then is strictly convex. This answers a question of C. Cowen for the case of analytic polynomials.

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Additional Information

**Muneo Cho**

Affiliation:
Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan

Email:
chiyom01@kanagawa-u.ac.jp

**Raúl E. Curto**

Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Email:
curto@math.uiowa.edu

**Woo Young Lee**

Affiliation:
Department of Mathematics, SungKyunKwan University, Suwon 440-746, Korea

Email:
wylee@yurim.skku.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-02-06628-5

Keywords:
Triangular Toeplitz contractions,
hyponormal Toeplitz operators

Received by editor(s):
September 7, 2000

Received by editor(s) in revised form:
July 2, 2001

Published electronically:
May 8, 2002

Additional Notes:
The second author’s work was partially supported by NSF research grant DMS-9800931

The third author’s work was partially supported by KOSEF research project No. R01-2000-00003

Communicated by:
David R. Larson

Article copyright:
© Copyright 2002
American Mathematical Society