On the tensor product of operators on Hilbert space

العناوين الأخرى

الجداء التنسوري للمؤثرات على فضاءات هلبرت

مقدم أطروحة جامعية

al-Tamimi, Maysaa Majid Abd al-Munim

مشرف أطروحة جامعية

Ahmad, Buthaynah Abd al-Hassun

الجامعة

جامعة بغداد

الكلية

كلية العلوم

القسم الأكاديمي

قسم الرياضيات

دولة الجامعة

العراق

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2005

الملخص الإنجليزي

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

التخصصات الرئيسية

الرياضيات

عدد الصفحات

73

قائمة المحتويات

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لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-601612