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Operators of Class $C_0$ with Spectra in Multiply Connected Regions, PDF eBook

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

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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.

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