Canadian mathematical bulletin | |
A Cohomological Property of $pi$-invariant Elements | |
M. Sangani Monfared2  M. Filali1  | |
[1] Department of Mathematical Sciences, University of Oulu, Oulu 90014, Finland;Department of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4 | |
关键词: Banach algebras; $pi$-invariance; derivations; representations; | |
DOI : 10.4153/CMB-2011-184-7 | |
学科分类:数学(综合) | |
来源: University of Toronto Press * Journals Division | |
【 摘 要 】
Let $A$ be a Banach algebra and $pi colon A longrightarrow mathscr L(H)$be a continuous representation of $A$ on a separable Hilbert space $H$with $dim H =frak m$. Let $pi_{ij}$ be the coordinate functions of$pi$ with respect to an orthonormal basis and suppose that for each$1le j le frak m$, $C_j=sum_{i=1}^{frak m}|pi_{ij}|_{A^*}lt infty$ and $sup_j C_jlt infty$. Under theseconditions, we call an element $overlinePhi in l^infty (frak m , A^{**})$ left $pi$-invariant if $acdot overlinePhi ={}^tpi (a) overlinePhi$ for all$ain A$. In this paper we prove a link between the existence of left $pi$-invariant elements and the vanishing of certainHochschild cohomology groups of $A$. Our results extend an earlierresult by Lau on $F$-algebras and recent results of Kaniuth-Lau-Pymand the second named author in the special case that $pi colon Alongrightarrow mathbf C$ is a non-zero character on $A$.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912050576981ZK.pdf | 23KB | download |