15782

14088

كارشناسي ارشد

آناليز رياضي

اصفهان : دانشگاه صنعتي اصفهان

1399

[هفت]، 71ص.

1399/07/05

كتابنامه

رياضي

رياضي

1399/07/06

2635557

Analysis on semidirect product of Banach algebras Aboozar Niknam amir niknam74@gmail com 2020 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Mehdi Nemati m nemati@cc iut ac irMSC 43A07 46H10 46H25 46H20 Keywords Banach algebras Banach module multiplier maximal ideal cyclic derivation weak amenability Abstract Let A and B be Banach algebras It is well known that the Cartesian product space A Bequipped with the L1 norm and coordinatewise operations is a Banach algebra In order toprovide new examples of Banach algebras as well as a wealth of counter examples in differ ent branches of functional analysis the construction of an algebra product on the Cartesianproduct space A B to make it a Banach algebra has been studied in a series of papers recently The first important paper related to this construction is Lau s paper 15 which he defined anew algebra product on the Cartesian product space A B for the case where B is the predualof a van Neumann algebra M such that the identity of M is a multiplicative linear functionalon B Later on Monfared 17 extended the Lau product to arbitrary Banach algebras Thisconstruction has many applications in different contexts see for examples 6 14 18 19 Moreover it is notable that such constructions are also investigated in commutative ring the ory and have been extensively studied in recent years see for examples 4 5 13 and thereferences therein On the other hand motivated by Wedderburn s principal theorem 1 splitting of Banachalgebra extensions has been a major question in the theory of Banach algebras and several re searchers have used the splitting of Banach algebra extensions as a tool for the study of Banachalgebras For example module extensions as generalizations of Banach algebra extensionswere introduced and first studied by Gourdeau 11 were used to show that amenability ofA 2 the second dual space of A implies amenability of A Filali and Eshaghi Gordji 7 usedtriangular Banach algebras to answer some questions asked by Lau and Ulger 16 Zhang 24 used module extensions to construct an example of a weakly amenable Banach algebrawhich is not 3 weakly amenable For some other applications of splitting of Banach algebraextensions we refer the reader to the references 2 3 9 23 Recall some notations Let A and A be Banach algebras such that A is a Banach A bimodule we say that the left and right actions of A on A are compatible if for each a b A and A ab a b ab a b a b a b and in the case where a a we say that A is a symmetric A bimodule Let A and A be Banach algebras such that A is a Banach A bimodule with compatible actions The amalgamated duplication of A along A denoted by A A is defined as the Cartesianproduct A A with the algebra product a b ab a b and with the norm a a

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