Weak topological centers and cohomological properties
Publish place: Caspian Journal of Mathematical Sciences، Vol: 11، Issue: 1
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_CJMS-11-1_022
تاریخ نمایه سازی: 15 اسفند 1401
Abstract:
Let B be a Banach A-bimodule. We introduce the weak topological centers of left module action and we show it by \tilde{{Z}}^\ell_{B^{**}}(A^{**}). For a compact group, we show that L^۱(G)=\tilde{Z}_{M(G)^{**}}^\ell(L^۱(G)^{**}) and on the other hand we have \tilde{Z}_۱^\ell{(c_۰^{**})}\neq c_۰^{**}. Thus the weak topological centers are different with topological centers of left or right module actions.In this manuscript, we investigate the relationships between two concepts with some conclusions in Banach algebras. We also have some application of this new concept and topological centers of module actions in the cohomological properties of Banach algebras, spacial, in the weak amenability and n-weak amenability of Banach algebras.
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Authors
Kazem Haghnejad Azar
University of Mohghegh Ardabili
Mostfa Shams
Islamic Azad University