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Operators of Class $C_0$ with Spectra in Multiply Connected Regions
 
Adele Zucchi Indiana University, Bloomington, IN
Front Cover for Operators of Class C_0 with Spectra in Multiply Connected Regions
Available Formats:
Electronic 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
Front Cover for Operators of Class C_0 with Spectra in Multiply Connected Regions
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  • Front Cover for Operators of Class C_0 with Spectra in Multiply Connected Regions
  • Back Cover for Operators of Class C_0 with Spectra in Multiply Connected Regions
Operators of Class $C_0$ with Spectra in Multiply Connected Regions
Adele Zucchi Indiana University, Bloomington, IN
Available Formats:
Electronic 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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1271997; 52 pp
    MSC: 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.

    Readership

    Graduate 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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Volume: 1271997; 52 pp
MSC: 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.

Readership

Graduate students and research mathematicians interested in operator theory.

  • Chapters
  • 1. Introduction
  • 2. Preliminaries and notation
  • 3. The class $C_0$
  • 4. Classification theory
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