15334

1506 دكتري

دكتري

محض

اصفهان : دانشگاه صنعتي اصفهان

1398

[هفت]، [101]ص.

محمود منجگاني

فريد بهرامي

مهدي نعمتي، حميدرضا افشين، عباس سالمي

1398/09/12

كتابنامه

رياضي

رياضي

1398/09/13

2582157

Majorization and its linear preservers on L1 X Shirin Moein s moein@math iut ac ir Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Seyed Mahmoud ManjeganiAdvisor Dr Farid Bahrami2010 15A45 15B51 26B25 26D15 47B65Keywords majorization doubly stochastic operators linear preserver entanglementAbstract This PHD thesis is based on the following papers Majorization of Integrable Functions and Its Linear Preservers Farid Bahrami Mahmoud Manjegani and Shirin Moein Submitted paper 2019 A simplified and unified generalization of some majorization results Shirin Moein Rajesh Pereira Sarah Plosker Journal of mathematical analysis and application 2019 Quasi doubly stochastic operator on l1 and Nielsen s Theorem Mahmoud Manjegani Shirin Moein Journal of Mathematical Physics 2019 عملگرھاي ن متصادفي دوگان و كاربرد آن در ف ز ك كوانتوم فر د ب رامي س د محمود منجگاني و ش ر ن مع ن م ج ل 1398 موجكھا و جبرخطي In the first section we provide a short history for majorization theory and preliminary definitions We first recall the definition of vector majorization if x y Rn we say x is majorized by y denotedx y if k k x yj k 1 n 1 j j 1 j 1 with equality when k n where x has been reordered so that x1 x2 x and similarly for ny A well known theorem of Hardy Littlewood and P lya states that x y is equivalent to the existenceof a doubly stochastic matrix S such that x Sy 12 Theorem 8 In the second section we introduce the semi doubly stochastic operator which is between doubly stochasticoperators and column stochastic operators so as to apply to characterized operator S on l1 such that Sfis majorized by f for every f l1 We present some classes of majorization preservers on l1 under semidoubly stochastic operators Moreover as application of our result in quantum physics the convertibilityof pure states of a composite system by local operations and classical communication has been considered The problem of entanglement transformation is related to the ability to convert a pure state of a com posite system to another pure state by Local Operations and Classical Communication LOCC Let H beseparable Hilbert space and B H be the set of all linear and bounded operators from H to itself F B Ha B Hb is called completely positive map when for all d N map Id F Md B Ha Md B Hb is positive Md denotes the algebra of d d matrices and Id refers to d d identity matrix

محمود منجگاني

فريد بهرامي

مهدي نعمتي، حميدرضا افشين، عباس سالمي