Weak spectral equivalence and weak spectral convergence. (English) Zbl 0559.47024

For the definitions of local spectrum, single valued extension property of an operator on a Banach space and related concepts see e.g., I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators (1968; Zbl 0189.442). In his paper, Rev. Roum. Math. Pur. Appl. 12, 733-736 (1967; Zbl 0156.382), F. H. Vasilescu introduces the notion of spectral equivalence or quasi-nilpotent equivalence of two operators. In the paper under review the author generalizes this notion to weak spectral equivalence of two operators. Most of the results in this paper are generalization of the results given in Vasilescu’s paper.
Reviewer: K.K.Oberai


47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
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