Other language title :
2n+1) - ﻣﻴﺎﻧﮕﻴﻦ ﭘﺬﻳﺮي ﻣﺪوﻟﻲ ﺿﻌﻴﻒ ﺟﺒﺮﻫﺎي ﺑﺎﻧﺎخ ﻣﺜﻠﺜﻲ روي ﺟﺒﺮﻫﺎي ﻧﻴﻢﮔﺮوﻫﻲ ﻣﻌﻜﻮس
Title of article :
(2n+1)-Weak Module Amenability of Triangular Banach Algebras on Inverse Semigroup Algebras
Author/Authors :
Nasrabadi, E Department of Mathematic - Faculty of Mathematic Science and Statistics - University of Birjand - Birjand, Islamic Republic of Iran , Ramezanpour, M School of Mathematics and Computer Science - Damghan University - Damghan, Islamic Republic of Iran , Aasaraai, A Department of Applied Mathematics - Faculty of Mathematical Sciences - University of Guilan - Rasht, Islamic Republic of Iran
Abstract :
Let S be a commutative (not necessary unital) inverse semigroup with the set of idempotents E then ℓ1(S) is a commutative Banach ℓ1(E)-module with canonical actions . Recently , it is shown that the triangular Banach algebra .... is (n)-weakly ℓ1(E)-module amenable , provided that M=ℓ1(S) and S is unital or E satisfies condition Dk for some D E ℕ. In this paper , we show that T is (2 n + 1)-weakly ℓ1(E)-module amenable , without any additional conditions on S and E, if M is a certain quotient space of ℓ1 (S).
Farsi abstract :
ﭼﻜﻴﺪهﻓﺮض ﻛﻨﻴﺪ S ﻳﻚ ﻧﻴﻢﮔﺮوه ﻣﻌﻜﻮس ﺟﺎﺑﺠﺎﻳﻲ ﻧﻪ ﻟﺰوﻣﺎً ﻳﻚدار( ﺑﺎ ﻣﺠﻤﻮﻋﻪ ﺧﻮد ﺗـﻮانE ﺑﺎﺷـﺪ. در اﻳـﻦ ﺣﺎﻟﺖ e 1 S ﻫﻤﺮاه ﺑﺎ ﻋﻤﻞﻫﺎي ﻃﺒﻴﻌﻲ ﻳﻚ e 1 E ﻣﺪول ﺑﺎﻧﺎخ ﺟﺎﺑﺠـﺎﻳﻲ اﺳـﺖ. اﺧﻴـﺮاً ﻧﺸـﺎن داده ﺷـﺪه ... e 1 s ﻣﻴﺎﻧﮕﻴﻦ ﭘﺬﻳﺮ ﻣﺪوﻟﻲ ﺿﻌﻴﻒ اﺳﺖ وﻗﺘﻲ )M=e 1 S و S ﻳﻜﺪار ﺑﺎﺷﺪ ﻳﺎ E ﺑﺮاي ﻋـﺪدي ﻣﺎﻧﻨـﺪ k e ℕ در ﺷﺮط D k ﺻﺪق ﻛﻨﺪ. در اﻳﻦ ﻣﻘﺎﻟﻪ ﻣﺎ ﻧﺸﺎن ﻣﻲ دﻫﻴﻢ ﻛﻪ T (2n + 1 - ﻣﻴﺎﻧﮕﻴﻦ ﭘـﺬﻳﺮ ) ( E ) e 1 -ﻣـﺪوﻟﻲ ﺿﻌﻴﻒ اﺳﺖ ﺑﺪون ﻫﻴﭻ ﺷﺮط اﺿﺎﻓﻲ روي S و E ، اﮔﺮ M ﻓﻀﺎﻳﻲ ﺧﺎرج ﻗﺴﻤﺘﻲ ﺧﺎﺻﻲ از )e 1 (S درﻧﻈـﺮ ﮔﺮﻓﺘﻪ ﺷﻮد.
Keywords :
(n)-weak module amenability , Inverse semigroup , Triangular Banach algebra , First module cohomology group , Weak module amenability
Journal title :
Journal of Sciences Islamic Republic of Iran
