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Paper   IPM / M / 16693
School of Mathematics
Title:   Smooth Cohomology For C* -Algebras
Author(s):
 1 Massoud Amini 2 Ahmad Shirinkalam
Status:   Published
Journal: Math. Commun.
Vol.:  26
Year:  2021
Pages:   29-40
Supported by:  IPM
Abstract:
In this paper, we define a notion of smooth cohomology for C* -algebras which admit a faithful trace. We show that if \A ⊆ B(\h) is a C* -algebra with a faithful normal trace τ on \A , the ultra-weak closure of A , and X is a normal dual operatorial \A -bimodule, then H1s(A,X)=H1(A ,Xτ) , where Xτ is a closed submodule of X that consists of the smooth elements.