Memoirs of the American Mathematical Society 1997; 52 pp; softcover Volume: 127 ISBN10: 0821806262 ISBN13: 9780821806265 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/127/607
 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. Readership Graduate students and research mathematicians interested in operator theory. Table of Contents  Introduction
 Preliminaries and notation
 The class \(C_0\)
 Classification theory
 Bibliography
