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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The single-valued extension property and spectral manifolds

Author: Shan Li Sun
Journal: Proc. Amer. Math. Soc. 118 (1993), 77-87
MSC: Primary 47A11; Secondary 47B40
MathSciNet review: 1156474
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Abstract: We discuss the relation between the single-valued extension property (that is, Dunford's property (A)) and spectral manifolds $ {X_T}(F)$ of a bounded linear operator. In particular, we prove that Dunford's property (C) implies the property (A). We also prove that if $ T \in B(X)$ has the property $ ({\beta ^{\ast}})$ introduced by Fong, then $ X_{{T^{\ast}}}^{\ast}(F) = {X_T}{(\mathbb{C}\backslash F)^ \bot }$ for every closed set $ F$ in the complex plane $ \mathbb{C}$.

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