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Operators of Class $C_0$ with Spectra in Multiply Connected Regions

Adele Zucchi Indiana University, Bloomington, IN
Available Formats:
Electronic ISBN: 978-1-4704-0192-4
Product Code: MEMO/127/607.E
52 pp
List Price: $41.00 MAA Member Price:$36.90
AMS Member Price: $24.60 Click above image for expanded view Operators of Class$C_0$with Spectra in Multiply Connected Regions Adele Zucchi Indiana University, Bloomington, IN Available Formats:  Electronic ISBN: 978-1-4704-0192-4 Product Code: MEMO/127/607.E 52 pp  List Price:$41.00 MAA Member Price: $36.90 AMS Member Price:$24.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1271997
MSC: Primary 47; Secondary 30;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries and notation
• 3. The class $C_0$
• 4. Classification theory
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Volume: 1271997
MSC: Primary 47; Secondary 30;

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.

• 3. The class $C_0$