arXiv:2610.35901v1 Announce Type: new Abstract: In this paper, we introduce and study the notion of character cyclic amenability for Banach algebras, which combines the cyclicity condition on derivations with the character-dependent module structure arising in character amenability. We establish several basic properties of this notion and investigate its behavior under standard Banach algebra constructions. In particular, we study character cyclic amenability for opposite algebras, projective tensor products, l1-direct sums, quotient algebras, dense homomorphic images, and theta-Lau products. We also provide examples illustrating the relationship between character cyclic amenability and other amenability-type properties, including examples showing that character cyclic amenability does not imply cyclic amenability. Finally, we characterize character cyclic amenability for module extension Banach algebras in terms of phi-cyclic derivations and derivations associated with the underlying Banach module.
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