Triangular Toeplitz contractions and Cowen sets for analytic polynomials期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Triangular Toeplitz contractions and Cowen sets for analytic polynomials

Authors:	Muneo Cho Raú l E. Curto Woo Young Lee

Affiliation:	Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan ; Department of Mathematics, University of Iowa, Iowa City, Iowa 52242 ; Department of Mathematics, SungKyunKwan University, Suwon 440-746, Korea

Abstract:	Let $mathfrak{L}_{N}$ be the collection of lower triangular Toeplitz matrices and let $mathfrak{T}_{N}$ be the collection of lower triangular Toeplitz contractions. We show that $mathfrak{T}_{N}$ is compact and strictly convex, in the spectral norm, with respect to $mathfrak{L}_{N}$ ; that is, $mathfrak{T}_{N}$ is compact, convex and $partial _{mathfrak{L}_{N}} mathfrak{T}_{N} subseteq text{rm {ext}},mathfrak{T}_{N}$ , where $partial _{mathfrak{L}_{N}}(cdot )$ and denote the topological boundary with respect to $mathfrak{L}_{N}$ 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 $G_{f}^{prime }:={gin H^{infty }(mathbb{T}): text{$g(0)=0$space and the Toeplitz operator $T_{f+bar g}$space is hyponormal}}$ , then $G_{f}^{prime }$ is strictly convex. This answers a question of C. Cowen for the case of analytic polynomials.

Keywords:	Triangular Toeplitz contractions hyponormal Toeplitz operators

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