• 호남수학학술지
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• 제43권1호
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• pp.68-77
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• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.1-19
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• 2024

In this paper, the notions of strong Connes amenability for certain products of Banach algebras and module extension of dual Banach algebras is investigated. We characterize χ ⊗ η-strong Connes amenability of projective tensor product ${\mathbb{K}}{\hat{\bigotimes}}{\mathbb{H}}$ via χ ⊗ η-σwc virtual diagonals, where χ ∈ 𝕂_* and η ∈ ℍ_* are linear functionals on dual Banach algebras 𝕂 and ℍ, respectively. Also, we present some conditions for the existence of (χ, θ)-σwc virtual diagonals in the θ-Lau product of 𝕂 ×_θ ℍ. Finally, we characterize the notion of (χ, 0)-strong Connes amenability for module extension of dual Banach algebras 𝕂 ⊕ 𝕏, where 𝕏 is a normal Banach 𝕂-bimodule.