Advances in Operator Theory

Projections and isolated points of parts of the spectrum

Pietro Aiena and Salvatore Triolo

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‎‎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.

Article information

Adv. Oper. Theory, Volume 3, Number 4 (2018), 868-880.

Received: 17 April 2018
Accepted: 13 July 2018
First available in Project Euclid: 27 July 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A10: Spectrum, resolvent
Secondary: 47A11‎ ‎47A53‎ ‎47A55

Kato decomposition ‎localized SVEP‎ ‎spectrum


Aiena, Pietro; Triolo, Salvatore. Projections and isolated points of parts of the spectrum. Adv. Oper. Theory 3 (2018), no. 4, 868--880. doi:10.15352/aot.1804-1348.

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