6484

6049

كارشناسي ارشد

رياضي محض ﴿آناليز هارمونيك﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1390

[هشت]، 100ص.: مصور

ص.ع. به فارسي و انگليسي

رسول نصر اصفهاني

فريد بهرامي

26/11/90

صابر ناصري، محمدرضا كوشش

1396/10/12

كتابنامه

علوم رياضي

رياضي

ID6049

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Approximate Characterization of Projectivity and Injectivity for Banach Modules Golnoosh Rouhani g Rouhani@math iut ac ir November 30 2011 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor DR Rasoul Nasr Isfahani isfahani@cc iut ac ir DR Farid Bahrami fbahrami@cc iut ac irAdvisor 2000 MSC 46M18 18G05 18G50Key words Projective Banach module Injective Banach module biprojective Banach al gebra bi at Banach algebra Amenable Banach algebra AbstractIn this thesis the properties of projective and injective Banach modules are investigated Also the approach of Ghahramani and Loy is extended to the setting of Banach modules by showingthat projective and injective Banach modules can be characterized in approximate terms Inorder to characterize projective and injective Banach modules in approximate terms it willbe convenient to give the de nition of uniform approximate morphism in A mod where Ais a Banach algebra Let X Y A mod A uniform approximate morphism X to Y is anet in B X Y such that a x a x 0 uniformly on bounded subsets of Aand X Similarly one de nes uniform approximate morphisms in mod A and A mod A In chapter four we show that a left Banach A mod P is projective if and only if for eachadmissible epimorphism X Y and morphism P Y in A mod there exists auniform approximate morphism in B X Y such that in the norm topology Also we proved that a left Banach A mod I is injective if and only if for each admissiblemonomorphism Y X and morphism Y I in A mod there exists a uniformapproximate morphism in B X Y such that in the norm topology As aresult it is proved that if for the Banach left A mod P there exists a projective left BanachA mod F an admissible epimorphism F P and a uniform approximate morphism in B P F such that 1P in the norm topology the P is projective In chapter ve applications of these approximate characterizations are given in locally compact groups we prove that if G is a locally compact group then G is amenable if and only if there exists auniform approximate morphism m in L G such that m 1 1 We also show thatthe proof of corollary 3 4 of the paper Pirkovskii A Yu Approximate characterization of projectivity and injectivity for Banach modules Math Proc Cambridge Philos soc 2007 143 375 385 is not correct and we give a new proof of this result and also generalize this result The Banach algebra A is uniformly approximately contractible respectively uniformly ap proximately amenable if for each Banach A bimodule X and each continuous derivationD A X respectively D A X there exists a net x in X respectively inX such that D lim adx in the norm topology Equivalently A is uniformly approx imately contractible respectively uniformly approximately amenable if for each BanachA bimodule X the topology on H1 A X respectively on H1 A X is trivial In this the sis by using injective modules and Ext groups we prove that each uniformly approximatelycontractible respectively uniformly approximately amenable Banach algebra is contractible respectively amenable Furthermore we proved that the Banach algebra A is amenableif and only if A has an approximate virtual diagonal It is proved that A is amenable ifand only if there exists a bounded net M in A A such that M a a and M a a M 0 uniformly on bounded subsets of A

رسول نصر اصفهاني

فريد بهرامي

صابر ناصري، محمدرضا كوشش