Journal article
Triangular Toeplitz contractions and Cowen sets for analytic polynomials
Proceedings of the American Mathematical Society, Vol.130(12), pp.3597-3604
12/01/2002
DOI: 10.1090/S0002-9939-02-06628-5
Abstract
Let ℒN be the collection of N × N lower triangular Toeplitz matrices and let T-fraktur signN be the collection of N × N lower triangular Toeplitz contractions. We show that T-fraktur signN is compact and strictly convex, in the spectral norm, with respect to ℒN; that is, T-fraktur signN is compact, convex and ∂ℒNT-fraktur sign;N ⊆ ext T-fraktur signN, where ∂ℒN(·) and ext(·) denote the topological boundary with respect to ℒN 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 f is an analytic polynomial and if G′f:= {g ∈ H∞(T): g(0) = 0 and the Toeplitz operator Tf+ḡ is hyponormal}, then G′f is strictly convex. This answers a question of C. Cowen for the case of analytic polynomials.
Details
- Title: Subtitle
- Triangular Toeplitz contractions and Cowen sets for analytic polynomials
- Creators
- Muneo Chō - Kanagawa UniversityRaúl E. Curto - University of Iowa, MathematicsWoo Young Lee - Seoul National University
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.130(12), pp.3597-3604
- DOI
- 10.1090/S0002-9939-02-06628-5
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Number of pages
- 8
- Language
- English
- Date published
- 12/01/2002
- Academic Unit
- Mathematics
- Record Identifier
- 9983985928502771
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