5560

334 دكتري

دكتري

رياضي محض، آناليز هارمونيك

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1389

[هفت]،98ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

رياضي

ID334 دكتري

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Homological Properties of Banach Modules Over Group Algebras sima Soltani Renani simasoltani@math iut ac ir August 9 2010 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Nasr Isfahani isfahani@cc iut ac ir Advisor Dr Farid Bahrami fbahrami@cc iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Abstract In this thesis for a Banach algebra A and non zero character on A we give some nec essary and su cient condition for left contractibility of A as well as several hereditary properties We also study relations between homological properties of some Banach left A modules left contractibility and right amenability of A We then characterize left character contractibility of various Banach algebras related to locally compact groups Fi nally we investigate some homological properties of L G L G LU C G and LU C G 0 0 as Banach left L1 G or M G modules such as atness injectivity and projectivity Key Words Banach algebra character amenable character contractible injectivity projectivity Banach left module locally compact group Introduction A Banach algebra A is called amenable if the rst cohomology group H 1 A X vanishes for all Banach A bimodules X Johnson 5 showed that the amenability of the group algebra L1 G for a locally compact group G is equivalent to the amenability of G however this equivalence does not remain true for the convolution semigroup algebra 1 S of a discrete semigroup S consider for example the additive semigroup N of natural numbers Motivated by this consideration Lau 7 introduced and investigated a large of class of Banach algebras which he called F algebras that is a Banach algebra L which is the predual of a W algebra M such that the identity element u of M is a character on L Later in 12 F algebras were termed Lau algebra A Lau algebra L was said to be left amenable if H 1 L X 0 for all Banach L bimodules X with the left action de ned by l x u l x for all l L and x X Lau 7 proved that 1 S is left amenable if and only if S is left amenable see also Lau and Wong 9 Let A be a Banach algebra and A 0 where A is the spectrum of A consisting of all characters from A into complex numbers The Banach algebra A is called left amenable if H 1 A X vanishes for all Banach A bimodules X for which the left module 1

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غلامحسين اسلام زاده، محمدرضا ودادي