5990

5599

كارشناسي ارشد

آناليز هارمونيك

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1389

[هفت]،120ص.

ص.ع.به فارسي و انگليسي

رسول نصر اصفهاني

سعيد مقصودي

11/3/90

فاطمه ابطحي، محمدرضا كوشش

رياضي

ID5599

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Maps preserving zero product on Banach algebras Jafar Soltani Farsani j soltanifarsani@math iut ac ir October 25 2010 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Nasr Isfahani isfahani@cc iut ac ir 2010 MSC 43 A 20 Key words Banach algebra Banach module Locally compact group Doubly power bounded element Map preserving zero product Weighted homomorphism Derivation Abstract A linear Map T from a Banach algebra A into another B preserves zero product if T a T b 0 where a b belongs to A are such that ab 0 This thesis is mainly concerned with the question Of whether every continuous linear surjective map T that preserves zero product is A weighted homomorphism This is indeed the case for a large class of Banach algebras including group algebras Our method involves continuous bilinear maps from A A into a Banach space X such that preserves zero product We prove that such a map necessarily satisfies a b a b For every a and b in A and in the closure of D A in the strong operator topology where D A is the subalgebra of the multiplier algebra of A generated by doubly power bounded elements This method is also shown to be useful for characterizing derivations through zero products At the end of our investigation we introduce the generalized derivations We will show that under appropriate situations some linear operators can be generalized derivations Also we will see that a generalized derivation can be a derivation if it s considered under appropriate consumptions

رسول نصر اصفهاني

سعيد مقصودي

فاطمه ابطحي، محمدرضا كوشش