Spectrum and related sets: a survey

Kulkarni, S. H.

doi:10.1007/s41478-019-00214-z

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2021

2024

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Cited by 3 publications

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“…Many of these definitions can be found in the book [1]. Some material in this section is also available in the review article [6].…”

Section: Preliminariesmentioning

confidence: 99%

$G_1$ class elements in a Banach algebra

Kulkarni¹

2021

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Let A be a complex unital Banach algebra with unit 1. AnHere d(z, σ(a)) denotes the distance between z and the spectrum σ(a) of a. Some examples of such elements are given and also some properties are proved. It is shown that a G 1 -class element is a scalar multiple of the unit 1 if and only if its spectrum is a singleton set consisting of that scalar. It is proved that if T is a G 1 class operator on a Banach space X, then every isolated point of σ(T ) is an eigenvalue of T . If, in addition, σ(T ) is finite, then X is a direct sum of eigenspaces of T .2010 Mathematics Subject Classification. 46B99, 47A05.

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“…Many of these definitions can be found in the book [1]. Some material in this section is also available in the review article [6].…”

Section: Preliminariesmentioning

confidence: 99%