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http://hdl.handle.net/20.500.12358/21390
TitleOn Linear Maps Preserving Spectrum, Spectral Radius and Essential Spectral Radius
Title in Arabicحول الدوال الخطية الحافظة للطيف قطر الطيف ولنصف قطر الطيف الاساسي
Abstract

In this thesis, we focus our study on a part of the linear maps on algebras of operators that preserve certain properties of operators. We study linear maps preserving spectrum. Let X and Y be Banach spaces. We show that a spectrum preserving surjective linear map ϕ from B(X) to B(Y) is either of the form ϕ(T) = ATA-1 for an isomorphism A of X onto Y or the form ϕ(T) = BT×B-1 for an isomorphism B of X/ onto Y. After this, we study linear maps preserving the spectral radius. Let X be a complex Banach space. We show that if ϕ: B(X) ⟶ B(X) is a surjective linear map such that T and ϕ(T) have the same spectral radius for every T ∈ B(X), then ϕ = cθ where θ is either an algebra-automorphism or an antiautomorphism of B(X) and c is a complex constant such that |c|=1. Finally, we characterize linear maps from B(H) onto itself that preserve the essential spectral radius. Where B(H) is the algebra of all bounded linear operators on an infinite dimensional complex Hilbert space H.

Authors
Alser, Huda A D
Supervisors
Asad, Asad Y
Typeرسالة ماجستير
Date2016
LanguageEnglish
Publisherالجامعة الإسلامية - غزة
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  • PhD and MSc Theses- Faculty of Science [445]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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