• 호남수학학술지
• /
• 제43권1호
• /
• pp.68-77
• /
• 2021

This paper considers pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. We characterize pseudo Jordan homomorphisms on module extensions of Banach algebras and triangular Banach algebras. Moreover, we define pseudo derivations on the above stated Banach algebras and characterize this new notion on those algebras.

• 호남수학학술지
• /
• 제42권1호
• /
• pp.37-48
• /
• 2020

We first define a new multiplication on triangular Banach algebras. Then we study amenability, weak amenability, biflatness and biprojectivity of these algebras.

• 호남수학학술지
• /
• 제42권1호
• /
• pp.105-121
• /
• 2020

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.

• 대한수학회보
• /
• 제51권3호
• /
• pp.765-771
• /
• 2014

Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.