Search results for "47A11"
showing 2 items of 2 documents
Projections and isolated points of parts of the spectrum
2018
In this paper, we relate the existence of certain projections, commuting with a bounded linear operator $T\in L(X)$ acting on Banach space $X$, with the generalized Kato decomposition of $T$. We also relate the existence of these projections with some properties of the quasi-nilpotent part $H_0(T)$ and the analytic core $K(T)$. Further results are given for the isolated points of some parts of the spectrum.
Weyl's Theorems and Extensions of Bounded Linear Operators
2012
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 $\overline T$ of $T$ (respectively, for $T$) entails that Weyl's theorem holds for $T$ (respectively, for $\overline T$).