پديد آورنده :
شهرابي فراهاني، مهدي
عنوان :
تصويرهاي انقباضي روي جبرهاي باناخ
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي محض﴿آناليز﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
رسول نصر اصفهاني
استاد مشاور :
غلامحسين اسلام زاده
توصيفگر ها :
جبر اندازه , جبر فوريه - اشتيليتس , گروه موضعا فشرده , خاصيت تومي ياما , اميد شرطي
تاريخ نمايه سازي :
20/4/91
استاد داور :
فاطمه ابطحي، محمدرضا كوشش
تاريخ ورود اطلاعات :
1396/09/14
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Contractive Projection on Banach Algebras Mehdi Shahrabi Farahani sh frahani@math iut ac ir March 3 2012 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr R Nasr Isfahani Isfahani@cc iut ac iradvisor Dr GH Eslamzadeh esslamzadeh@shirazu ac ir2000 MSC 47H05 43A25 46J10 46L05 Key words Contractive Projection Banach Algebras Locally Compact Group Tomiyama Property Con ditional expectation Abstract In this thesis we give an expanded account of contractive projection on Bannach algebrasbased on an article by lau and loy Let X S be a probability space and T a subalgebraof S The conditional expectation operator E T L1 X S L1 X T is determinedby the relation T E T f d T f d for E T and all f L1 X S Existence anduniqueness of E T follow from the Radon Nikodym theorem In particular uniqueness showsthat E T is idempotent and since E T 1 E T is a contractive projection An easyargument withe simple functions also shows the fundamental relation E T f g g T f f L1 X S g L X T Slightly more generally suppose in the above situation thatS T is xed and k 0 is S measurable and satis es T kd T XS d for T T sothat E T k XS Then again f k E T f is a contractive projection on L X S A Grothendieck has proved that if a projection in an L1 space is contractive i e it has norm 1 then its range is isometric to an L1 space Later under the assumption that X S is a nite measure space R G Douglas has given a complete characterization of contractiveprojections in L1 X S related closely to the notion of conditional expectation In factthe general form of a contractive projection on L1 X S is U k E T U V for some unimodular S measurable where U f f and V is a related contraction with V 2 0 Douglas results have been extended by T Ando for Lp space 1 p he has proventhat a contractive projection in an Lp space 1 p over a nite measure space is similarto a conditional expectation and hence its range is isometric to an Lp space Obviously therange of a contractive projection in a separable Lp space has the same structure Contractiveprojections have been studied in other situations see for example 1 14 16 33 41 In manycases it is known that the range of such projection on certain algebras is often imbued withalgebraic structure of its own and the projection itself is a conditional expectation operator The current thesis has the same avor though from the di erent perspective of hypothesisingalgebraic conditions on the range In the algebra setting an idempotent operator P on analgebra A is a conditional expectation if P abc aP b c a c P A b A Thus A P is a non commutative probability space in the sense of up There are several equivalentconditions relevant to our discussion in particular the form up is often more convenient touse Let a x ax denote left multiplication by a In this thesis we shall study contractiveprojections whose range is a subalgebra on various classes of Bannach algebras particularlythose associated with locally compact groups 1
استاد راهنما :
رسول نصر اصفهاني
استاد مشاور :
غلامحسين اسلام زاده
استاد داور :
فاطمه ابطحي، محمدرضا كوشش
