| eBook ISBN: | 978-1-4704-0192-4 |
| Product Code: | MEMO/127/607.E |
| List Price: | $41.00 |
| MAA Member Price: | $36.90 |
| AMS Member Price: | $24.60 |
| eBook ISBN: | 978-1-4704-0192-4 |
| Product Code: | MEMO/127/607.E |
| List Price: | $41.00 |
| MAA Member Price: | $36.90 |
| AMS Member Price: | $24.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 127; 1997; 52 ppMSC: 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 non-trivial 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries and notation
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3. The class $C_0$
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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 non-trivial 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
