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On spectra of operators of finite strict multiplicity. (English) Zbl 0771.47001
Summary: It is proved that if an operator \(T\) on a Banach space generates an operator algebra of strict multiplicity \(n\) satisfying condition \(S_ n\), then the spectrum of its adjoint consists entirely of eigenvalues and corresponding eigenspaces are all \(n\)-dimensional, and in addition, if \(X\) is reflexive, then any \(\lambda\) in \(\tau(T)\) with \(|\lambda|=\| T\|\) is an isolated point of \(\sigma(T)\). Some non-normal operators in such algebras on a Hilbert space are also discussed.

MSC:
47A10 Spectrum, resolvent
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