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Operators of Class $C_0$ with Spectra in Multiply Connected Regions PDF
by Adele Zucchi
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.
Information
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Download - Immediately Available
- Format:PDF
- Pages:52 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470401924
Information
-
Download - Immediately Available
- Format:PDF
- Pages:52 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470401924