Honam Mathematical Journal (호남수학학술지)

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GENERALIZED COHOMOLOGY GROUP OF TRIANGULAR BANACH ALGEBRAS OF ORDER THREE

  • Received : 2019.04.13
  • Accepted : 2019.06.27
  • Published : 2020.03.25
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Abstract

The main result of this article is to factorize the first (σ, τ)-cohomology group of triangular Banach algebra 𝓣 of order three with coefficients in 𝓣 -bimodule 𝓧 to the first (σ, τ)-cohomology groups of Banach algbras 𝓐, 𝓑 and 𝓒, where σ, τ are continuous homomorphisms on 𝓣. As a direct consequence, we find necessary and sufficient conditions for 𝓣 to be (σ, τ)-weakly amenable.

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References

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