The First and Second Hochschild Cohomology Groups of Banach Algebras with Coefficients in Special Symmetric Bimodules
| Autor: | V. Khodakarami, Hoger Ghahramani, E. Feizi |
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| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Functional Analysis
Applied Mathematics 010102 general mathematics Hausdorff space Mathematics::General Topology Operator theory 01 natural sciences Cohomology Combinatorics Computational Mathematics Computational Theory and Mathematics 0103 physical sciences 010307 mathematical physics Locally compact space 0101 mathematics Mathematics::Representation Theory Banach *-algebra Mathematics |
| Zdroj: | Complex Analysis and Operator Theory. 14 |
| ISSN: | 1661-8262 1661-8254 |
| DOI: | 10.1007/s11785-020-01027-w |
| Popis: | Let A be a Banach algebra and $$\phi $$ be a character on A. In this paper we consider the class $${\mathscr {S}}{\mathscr {M}}^{A}_{\phi }$$ of Banach A-bimodules X for which the module actions of A on X is given by $$a \cdot x = x \cdot a = \phi (a)x $$ ( $$a \in A, x \in X$$ ) and we study the first and second continuous Hochschild cohomology groups of A with coefficients in $$X\in {\mathscr {S}}{\mathscr {M}}^{A}_{\phi }$$ . We obtain some sufficient conditions under which $$H^1(A,X)=\lbrace 0 \rbrace $$ and $$H^2(A,X)$$ is Hausdorff, where $$X\in {\mathscr {S}}{\mathscr {M}}^{A}_{\phi }$$ . We also consider the property that $$H^1(A,X)=\lbrace 0 \rbrace $$ for every $$X\in {\mathscr {S}}{\mathscr {M}}^{A}_{\phi }$$ and get some conclusions about this property. Finally, we apply our results to some Banach algebras related to locally compact groups. |
| Databáze: | OpenAIRE |
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