Abstract
We study on the second cohomology of the module extension Banach algebra A⊕1X, where A is a Banach algebra and X is a Banach A-bimodule. We characterize the defined 2-cocycles and 2-coboundaries on A⊕1X and as an interesting result we show that when H2(A,A)=0, then H2(A⊕1A,A⊕1A)=QM(A), where QM(A) is the set of quasi-multipliers on A. Also, we give some examples related to vanishing and nonvanishing of the second cohomology of various module extensions of Banach algebras.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
