On linear maps preserving spectrum, spectral radius and essential spectral radius
Other Title(s)
حول الدوال الخطية الحافظة للطيف، لنصف قطر الطيف و لنصف قطر الطيف الأساسي
Dissertant
al-Sirr, Huda Abd al-Karim Diyab
Thesis advisor
Comitee Members
Safi, Ziyad Rizq
al-Mabhuh, Ahmad Abd al-Rauf
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2016
English 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.
Main Subjects
No. of Pages
65
Table of Contents
Table of contents.
Abstract.
Introduction.
Chapter One : Preliminaries.
Chapter Two : Linear maps preserving spectrum.
Chapter Three : Linear maps preserving spectral radius.
Chapter Four : Linear maps preserving essential spectral radius.
References.
American Psychological Association (APA)
al-Sirr, Huda Abd al-Karim Diyab. (2016). On linear maps preserving spectrum, spectral radius and essential spectral radius. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-724356
Modern Language Association (MLA)
al-Sirr, Huda Abd al-Karim Diyab. On linear maps preserving spectrum, spectral radius and essential spectral radius. (Master's theses Theses and Dissertations Master). Islamic University. (2016).
https://search.emarefa.net/detail/BIM-724356
American Medical Association (AMA)
al-Sirr, Huda Abd al-Karim Diyab. (2016). On linear maps preserving spectrum, spectral radius and essential spectral radius. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-724356
Language
English
Data Type
Arab Theses
Record ID
BIM-724356