**Memoirs of the American Mathematical Society**

1997;
52 pp;
Softcover

MSC: Primary 47;
Secondary 30

Print ISBN: 978-0-8218-0626-5

Product Code: MEMO/127/607

List Price: $41.00

AMS Member Price: $24.60

MAA member Price: $36.90

**Electronic ISBN: 978-1-4704-0192-4
Product Code: MEMO/127/607.E**

List Price: $41.00

AMS Member Price: $24.60

MAA member Price: $36.90

# Operators of Class \(C_{0}\) with Spectra in Multiply Connected Regions

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*Adele Zucchi*

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.