Conditions Implying Self-adjointness of Operators

Author： Jeon In  

Publisher： Springer Publishing Company

ISSN： 0378-620X

Source： Integral Equations and Operator Theory, Vol.61, Iss.4, 2008-08, pp. : 549-557

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Abstract

In this paper, we show that if $$T in {mathcal{B}}({mathcal{H}})$$ is a quasi-class A operator and S is an arbitrary operator for which $$0 otin overline{W(S)}$$ and ST = T*S, then T is self-adjoint, and we also show that quasisimilar quasi-class A operators have equal spectra and essential spectra.

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