Operators of Class Co With Spectra in Multiply Connected Regions (Memoirs of the American Mathematical Society)

Zucchi, Adele

ISBN 10: 0821806262 / ISBN 13: 9780821806265

Published by Amer Mathematical Society 0, 1997

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Bibliographic Details

• Title: Operators of Class Co With Spectra in Multiply Connected Regions (Memoirs of the American Mathematical Society)
• Publisher: Amer Mathematical Society 0
• Publication Date: 1997
• Language: English
• ISBN 10: 0821806262
• ISBN 13: 9780821806265
• Binding: paperback
• Condition: Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

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Synopsis

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.