On the tensor product of operators on Hilbert space
Other Title(s)
الجداء التنسوري للمؤثرات على فضاءات هلبرت
Dissertant
al-Tamimi, Maysaa Majid Abd al-Munim
Thesis advisor
Ahmad, Buthaynah Abd al-Hassun
University
University of Baghdad
Faculty
College of Science
Department
Mathematics Department
University Country
Iraq
Degree
Master
Degree Date
2005
English Abstract
Let H1andH2 be two vector spaces over a field K the formal linear combination of pairs ( f , g)is denoted by ( ) F H1 , H2 ( ) F H1 , H2 = ( ) ïþ ïý ü ïî ïí ì = Î Î Î å= n J c j f j g j c j K f j H g j H j n 1 , : , 1, 2 , 1,K, is a vector space.
Let N be the subspace of ( ) F H1 , H2 spanded by the elements of the form.
( ) ÷ ÷ø ö ç çè æ åå - ´ å å = = = = n j m k j j k k n j m k a jbk f j gk a f b g 1 1 1 1 , 1 , The quotient space.
( ) H1 Ä H2 = F H1,H2 N is called the algebraic tensor product.
H1 Ä H2 is a pre-Hilbert space with inner product defined by å ( Ä ) å ¢ ( ¢ Ä ¢ ) = = = m k k k k n j c j f j g j c f g 1 1 , åå = = ¢ ¢ ¢ n j m k c jck f j fk g j gk 1 1 1 2 , , The completion of H1 Ä H2 is called the tensor product of the Hilbert spaces H1,H2 and denoted by 1 2 H Ĉ H .
Robert, I.
showed that every operator A on the Hilbert space 1 2 H Ĉ H can be written as tensor product of two operators A1andA2 and denoted by A1 Ä A2 is defined by u Ä w, A(v Ä z) = u, A1v w, A2 z = u Ä w, A1v Ä A2 z for all u,vÎ H1 and w, z,ÎH2 In this thesis we study some properties of tensor product of operators defined on 1 2 H Ĉ H where each H1andH2 is separable Hilbert space and look for the relation between tensor products of operators with some kind of operators.
Also we study the identification between the elementary operator with Ä *A1 A2 and we can study the property of Ä *A1 A2 by studying the propriety of t A1,A1 (X ) Throughout this thesis we exhibits some known result ,with more details ,give proofs for other ones ,many results are
Main Subjects
No. of Pages
73
Table of Contents
Table of contents.
Abstract.
Abstract in Arabic.
Introduction.
Chapter One : Some preliminary concepts.
Chapter Two : Some properties of operators that are invariant under tensor product part I.
Chapter Three : Some properties of operators that are invariant under tensor product part II.
References.
American Psychological Association (APA)
al-Tamimi, Maysaa Majid Abd al-Munim. (2005). On the tensor product of operators on Hilbert space. (Master's theses Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-601612
Modern Language Association (MLA)
al-Tamimi, Maysaa Majid Abd al-Munim. On the tensor product of operators on Hilbert space. (Master's theses Theses and Dissertations Master). University of Baghdad. (2005).
https://search.emarefa.net/detail/BIM-601612
American Medical Association (AMA)
al-Tamimi, Maysaa Majid Abd al-Munim. (2005). On the tensor product of operators on Hilbert space. (Master's theses Theses and Dissertations Master). University of Baghdad, Iraq
https://search.emarefa.net/detail/BIM-601612
Language
English
Data Type
Arab Theses
Record ID
BIM-601612
