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Operators of Class \(C_0\) with Spectra in Multiply Connected Regions
Adele Zucchi, Indiana University, Bloomington, IN

Memoirs of the American Mathematical Society
1997; 52 pp; softcover
Volume: 127
ISBN-10: 0-8218-0626-2
ISBN-13: 978-0-8218-0626-5
List Price: US$41
Individual Members: US$24.60
Institutional Members: US$32.80
Order Code: MEMO/127/607
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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.

Table of Contents

  • Introduction
  • Preliminaries and notation
  • The class \(C_0\)
  • Classification theory
  • Bibliography
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