Electronic ISBN:  9781470401924 
Product Code:  MEMO/127/607.E 
52 pp 
List Price:  $41.00 
MAA Member Price:  $36.90 
AMS Member Price:  $24.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 127; 1997MSC: Primary 47; Secondary 30;
Let \(\Omega\) be a bounded finitely connected region in the complex plane, whose boundary \(\Gamma\) consists of disjoint, analytic, simple closed curves. The author considers linear bounded operators on a Hilbert space \(H\) having \(\overline \Omega\) as spectral set, and no normal summand with spectrum in \(\gamma\). For each operator satisfying these properties, the author defines a weak\(^*\)continuous functional calculus representation on the Banach algebra of bounded analytic functions on \(\Omega\). An operator is said to be of class \(C_0\) if the associated functional calculus has a nontrivial kernel. In this work, the author studies operators of class \(C_0\), providing a complete classification into quasisimilarity classes, which is analogous to the case of the unit disk.
ReadershipGraduate students and research mathematicians interested in operator theory.

Table of Contents

Chapters

1. Introduction

2. Preliminaries and notation

3. The class $C_0$

4. Classification theory


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Let \(\Omega\) be a bounded finitely connected region in the complex plane, whose boundary \(\Gamma\) consists of disjoint, analytic, simple closed curves. The author considers linear bounded operators on a Hilbert space \(H\) having \(\overline \Omega\) as spectral set, and no normal summand with spectrum in \(\gamma\). For each operator satisfying these properties, the author defines a weak\(^*\)continuous functional calculus representation on the Banach algebra of bounded analytic functions on \(\Omega\). An operator is said to be of class \(C_0\) if the associated functional calculus has a nontrivial kernel. In this work, the author studies operators of class \(C_0\), providing a complete classification into quasisimilarity classes, which is analogous to the case of the unit disk.
Graduate students and research mathematicians interested in operator theory.

Chapters

1. Introduction

2. Preliminaries and notation

3. The class $C_0$

4. Classification theory