پديد آورنده :
خاطرويسي، ميلاد
عنوان :
مشتقات تعميم يافته در برخي از جبرهاي پيچشي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
استاد راهنما :
مهدي نعمتي
استاد مشاور :
اقبال قادري
توصيفگر ها :
گروه فشرده موضعي , جابجاگر , مشتق جردن , مشتق تعميم يافته , k−شبه جابجاگر , ضرب آرنز
استاد داور :
محمود منجگاني، سيما سلطاني
تاريخ ورود اطلاعات :
1399/11/30
تاريخ ويرايش اطلاعات :
1399/12/03
چكيده انگليسي :
Generalized derivations on some convolution algebras Milad khatervaisie m khatervaisie@math iut ac ir 2020 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Mehdi Nemati m nemati@iut ac irMSC 16W 25 43A15 47B47 Keywords Locally compact abelian groups Generalized derivations Jordan derivation k centralizingmappings Singer Wermer conjecture Orthogonal generalized derivations Abstract Let G be a locally compact abelian group with a fixed Haar measure and let L1 G be the group algebra of Gequipped with the convolution product and the norm 1 we denote by L G the subspace of all functions 0f L G the usual Lebesgue space equipped with the essential supremum norm that for each thereis a compact subset K of G for which f G K where G K denotes the characteristic function G K on G It is well known that the subspace L G is a 0topologically introverted subspace of L G that is for each n L G and f L G the function 0 0nf L G where 0 nf n f f f for all L1 G Hence L G is a Banach algebra with the first Arens product defined by the formula 0 m n f m nf for all m n L G and f L G By rad L G we denote the Jacobson radical of L G 0 0 0 0A linear map d L G L G is called a derivation of L G if 0 0 0 d m n d m n m d n for all m n L G A linear map D L G L G is called a generalized derivation of 0 0 0 G if there exists a derivation d of L G such thatL0 0 D m n D m n m d n for all m n L G The derivation d is called the associated derivation of D 0In 1955 Singer and Wermer 19 initiated the study of range inclusion results for derivations on Banach algebrasand proved that d A rad A when A is a commutative Banach algebra and d is continuous In particular d 0 when A is semisimple They also conjectured that the assumption of continuity is unnecessary This becameknown as the Singer Wermer conjecture and was finally proved in 1987 by Thomas 21 Of course the same resultdoes not hold in non commutative Banach algebras but there have been many non commutative extensions ofSinger Wermer theorem in the literature 24 25 26 14 27 11 In 15 Posner gave a non commutative versionof the Singer Wermer theorem for prime rings He proved that the zero map is the only centralizing derivation ona non commutative prime ring In harmonic analysis for a locally compact group G the algebra L G equipped with the Arens product is 0neither a commutative Banach algebra nor a prime ring when G is a non discrete group Thus it is of interestto determine when a generalized derivation on L G maps L G into the radical In this thesis we study 0 0
استاد راهنما :
مهدي نعمتي
استاد مشاور :
اقبال قادري
استاد داور :
محمود منجگاني، سيما سلطاني
