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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