A bounded operator $T\in L(X)$, $X$ a Banach space, is said to satisfy Weyl's theorem if the set of all spectral points that do not belong to the Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues and having finite multiplicity. In this article we give sufficient conditions for which Weyl's theorem for an extension of T entails that Weyl's theorem holds for $T
Aiena, P., Cho, M., Zhang, L. (2012). Weyl's theorems and extensions of bounded linear operators. TOKYO JOURNAL OF MATHEMATICS, 35(Issue 2), 279-289 [10.3836/tjm/1358951318].
Weyl's theorems and extensions of bounded linear operators
AIENA, Pietro;
2012-01-01
Abstract
A bounded operator $T\in L(X)$, $X$ a Banach space, is said to satisfy Weyl's theorem if the set of all spectral points that do not belong to the Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues and having finite multiplicity. In this article we give sufficient conditions for which Weyl's theorem for an extension of T entails that Weyl's theorem holds for $T
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