### Projections and isolated points of parts of the spectrum

#### Abstract

‎‎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

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

Dates
Accepted: 13 July 2018
First available in Project Euclid: 27 July 2018

https://projecteuclid.org/euclid.aot/1532656921

Digital Object Identifier
doi:10.15352/aot.1804-1348

Mathematical Reviews number (MathSciNet)
MR3856179

Zentralblatt MATH identifier
06946384

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

#### Citation

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. https://projecteuclid.org/euclid.aot/1532656921

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