# Operators of Class Co with Spectra in Multiply Connected Regions - Memoirs of the American Mathematical Society (Paperback)

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Paperback 52 Pages / Published: 30/05/1997
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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.

Publisher: American Mathematical Society
ISBN: 9780821806265
Number of pages: 52
Weight: 132 g

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