E-resources
Peer reviewed
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Ghasemi, M.; Mehdipour, M. J.
Bulletin of the Malaysian Mathematical Sciences Society, 05/2021, Volume: 44, Issue: 3Journal Article
Let A and B be Banach algebras with σ ( B ) ≠ ∅ . Let θ , ϕ , γ ∈ σ ( B ) and Der ( A × θ ϕ , γ B ) be the set of all linear mappings d : A × B → A × B satisfying d ( ( a , b ) · θ ( x , y ) ) = d ( a , b ) · ϕ ( x , y ) + ( a , b ) · γ d ( x , y ) for all a , x ∈ A and b , y ∈ B . In this paper, we characterize elements of Der ( A × θ ϕ , γ B ) in the case where A has a right identity. We then investigate the concept of centralizing for elements of Der ( A × θ ϕ , γ B ) and determine dependent elements of Der ( A × θ ϕ , γ B ) . We also apply some results to group algebras.
