In this paper, we relate the existence of certain projections, commuting with a bounded linear operator T ∈ 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 H0(T) and the analytic core K(T). Further results are given for the isolated points of some parts of the spectrum.
Aiena, P., Triolo, S. (2018). Projections and isolated points of parts of the spectrum. ADVANCES IN OPERATOR THEORY, 3(4), 868-880 [10.15352/aot.1804-1348].
Projections and isolated points of parts of the spectrum
Aiena, Pietro;Triolo, Salvatore
2018-01-01
Abstract
In this paper, we relate the existence of certain projections, commuting with a bounded linear operator T ∈ 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 H0(T) and the analytic core K(T). Further results are given for the isolated points of some parts of the spectrum.
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