Spectrum of the products of operators and compact perturbations

Gong, Wei Bang; Han, De Guang

doi:10.1090/S0002-9939-1994-1197538-6

Spectrum of the products of operators and compact perturbations
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by Wei Bang Gong and De Guang Han PDF

Proc. Amer. Math. Soc. 120 (1994), 755-760 Request permission

Abstract:

In this paper we will give a complete characterization of the operator $B$ which satisfies the spectral condition $\sigma (AB) = \sigma (BA)$ (resp. ${\sigma _e}(AB) = {\sigma _e}(BA))$ for every $A$ in $L(H)$ and also a spectral characterizations of the product of finitely many normal (resp. essentially normal) operators.

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