12707

11631

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1396

Viii,[62]ص.: مصور

ص.ع. به فارسي و انگليسي

محمود منجگاني

فريد بهرامي

فارسي به انگليسي

رسول نصر اصفهاني، مهدي نعمتي

1396/05/30

كتابنامه

علوم رياضي

رياضي

ID11631

Majorisation and the Carpenter sTheorem in in nite dimensional Hilbert spaces Mahboobeh Limooei M Limooei@math iut ac ir 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Seyed Mahmoud Manjegani manjgani@cc iut ac ir Advisor Dr Fared Bahrami @cc iut ac ir 2010 MSC 05C15 53C42 Keywords Majorisation Schur Horn theorem Carpenter s theorem in in nite dimensionalHilbert spaces AbstractIn this thesis we discuss Kadison s Carpenter s Theorems and their relation to majorisation in in nitedimensional Hilbert spaces As it is well known the Pythagorean Theorem states that If a and b are the lengths of two sidesof a right angle in the right triangle and c is the length of the hypotenuse of the triangle then a2 b2 c2Let H be a Hilbert space of any dimension and ei be an orthonormal basis for H If H then ei ei If x H then x ci ei where the equality refers to convergence of inite subsums to x in H ByParseval equality x ci 2 This is a direct extension of the Pythagorean Theorem to Hilbert space H of any dimension The positive numbers a and b are the lengths of the sides of a right triangle with hypotenuse of

محمود منجگاني

فريد بهرامي

رسول نصر اصفهاني، مهدي نعمتي