پديد آورنده :
قادري، اقبال
عنوان :
آناليز حاصلضرب هاي خاص از جبر هاي باناخ
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿ آناليز﴾
محل تحصيل :
اصفهان:دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
[هفت] ، 96، [II] ص.
يادداشت :
ص . ع .به فارسي و انگليسي
استاد راهنما :
رسول نصر اصفهاني
توصيفگر ها :
توسيع , ايدآل , نرم محدب , نرم منظم , جبرهاي نرم دار
تاريخ نمايه سازي :
8/4/88
استاد داور :
سعيد مقصودي ، محمود منجگاني
چكيده فارسي :
به فارسي و انگليسي : قابل رويت در نسخه ديجيتال
چكيده انگليسي :
Analysis on Certain Products of Banach Algebras Eghbal Ghaderi ghaderi@math iut ac ir March 8 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Rasoul Nasr Isfahani isfahani@cc iut ac ir2000 MSC Primary 46H20 Secondary 46H10 46J20 46J05 Key words Banach algebras extensions ideals convex norm regular norm normed algebras AbstractIn this thesis we present an expanded account of Analysis on Certain Products of BanachAlgebras based on some articles by Monfared 2006 and Arhippainen and Kauppi 2000 Let A B be Banach algebras with B and given B We recall that thespectrum B of a Banach algebra B is the set of all non zero multiplicative linear function als on B We de ne a product A B which is a strongly Banach algebra extension of B byA The product A B of Banach algebras de ned in this thesis were rst introduced by T Lau for a special class of Banach algebras that are pre duals of von Neumann algebras andfor which the identity of the dual is a multiplicative linear functional In this thesis we showthat these products can be de ned for Banach algebras in a fairly general setting We obtaincharacterizations of bounded approximate identities spectrum topological center minimalidempotents and study the ideal structure of these products by assuming B to be a Banachalgebra in C0 X whose spectrum can be identi ed with X we apply our results to harmonicanalysis and study the questions of spectral synthesis and primary ideals Next we consider norms on commutative algebra as a space and study such norms oncommutative algebras for which the multiplication is separately continuous By comparinga given norm to its operator seminorm op we get two constants m the modulusof m convexity and r the modulus of regularity We study how these constants areconnected to the m convexity and to the A convexity of In particular we give a con cept of an irregular norm and study some properties of such norms Further we will givea generalization of the famous theorem of Gelfand which states that a complete A convexnorm is always equivalent to some m convex norm and if the algebra has a unitelement e this norm can be chosen so that e 1 Finally let A be an algebra without unit If is a complete regular norm on A can beextended to an algebra norm on the unitization A 1 C in many ways It is known that amongthe regular extensions of to the unitization of A there exists a minimal operator exten sion and maximal l1 extension which are known to be equivalent We shall show that thebest upper bound for the ratio of these two extensions is exactly 3 This improves the resultsrepresented by A K Gaur and Z V Kovarik and later by T W Palmer Equivalence ofvarious norms on the unitization of a nonunital Banach algebra is established with bounds 1 and 6 exp 1 uniform over the class of such algebras A tighter bound 3 is obtained inC algebras for elements with Hermitian nonunital parts 1
استاد راهنما :
رسول نصر اصفهاني
استاد داور :
سعيد مقصودي ، محمود منجگاني
