توصيفگر ها :
تابع يكنواي عملگري , تابع محدب عملگري , عملگرهاي كوترنيوني , نامساوي يانگ , نامساوي معكوس يانگ , ميانگين عملگري , قضيه طيفي , مقادير ويژه , اطلاعات كلاسيك , اطلاعات كوانتوم , مكانيك كوانتوم , آنتروپي
چكيده انگليسي :
Inequalities in Operator Algebras with Applications Asghar Norouzi asghar norouzi@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Seyed Mahmoud Manjegani manjgani@cc iut ac ir Advisor Dr Farid Bahrami fbahrami@cc iut ac ir 2010 MSC 05C15 53C42 Keywords operator inequality operator monotone function operator convex function quater nionic operators Young inequality inverse Young inequality operator mean spectral theorem eigen values spectrum classical informations quantum informations quantum mechanics entropy AbstractSome of the most important inequalities as well as some equalities in complex numbers admit general isations in operator context The equality zw z w the triangle inequality z w z w andthe arithmetic geometric mean inequality zw 1 z 2 w 2 are all in evidence see 28 and 9 2for generalisations of the second and the third one to operators A generalization of the arithmetic geometric mean inequality is the Young inequality 1p1q zw z w 6 6 p qin which p q 1 are conjugate exponents And where equality holds if and only if z p w q The Young inequality 6 6 was extended to complex operators in the special case p q 2 byBhatia and Kittaneh in 9 and in the general case by Ando in 1 as follows Theorem 1 If H is a nite dimensional complex Hilbert space then for each pair A and B of linear
