Remarks on the Peripheral Spectrum of Operators in Hilbert Spaces

Bernard Mutuku Nzimbi; Faith Muthoni Mwangi; Stephen Wanyonyi Luketero

doi:https://doi.org/10.14445/22315373/IJMTT-V68I11P506

International Journal of Mathematics Trends and Technology

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Volume 68 | Issue 11 | Year 2022 | Article Id. IJMTT-V68I11P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I11P506

Remarks on the Peripheral Spectrum of Operators in Hilbert Spaces

Bernard Mutuku Nzimbi, Faith Muthoni Mwangi, Stephen Wanyonyi Luketero

Received	Revised	Accepted	Published
03 Oct 2022	05 Nov 2022	19 Nov 2022	30 Nov 2022

Abstract

In this paper, we investigate the peripheral spectrum of some operators, which is a boundary-type subset of the spectrum of a bounded linear operator in a separable complex Hilbert space. We characterize this set for operators in some equivalence relations and give conditions under which equivalent classes of operators have the same peripheral spectrum.

Keywords

Resolvent, Spectrum, Spectral radius, Peripheral spectrum, Peripheral point spectrum.

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Citation :

Bernard Mutuku Nzimbi, Faith Muthoni Mwangi, Stephen Wanyonyi Luketero, "Remarks on the Peripheral Spectrum of Operators in Hilbert Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 11, pp. 63-72, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I11P506