Operators of class C[0] with spectra in multiply connected regions
Author(s)
Bibliographic Information
Operators of class C[0] with spectra in multiply connected regions
（Memoirs of the American Mathematical Society, no. 607）
American Mathematical Society, 1997
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Note
"May 1997, volume 127, number 607 (third of 4 numbers)"
Includes bibliography (p. 51-52)
Description and Table of Contents
Description
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.
Table of Contents
Introduction Preliminaries and notation The class $C_0$ Classification theory Bibliography.
by "Nielsen BookData"