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A note on derivations into annihilators of the ideals of banach algebras

  • Ebrahim Nasrabadi EMAIL logo , Mohammad Reza Miri and Javad Momeni
Published/Copyright: June 9, 2025
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Abstract

In a recent study, Teymouri et al. [Derivations into annihilators of the ideals of Banach algebras, Demonstr. Math. 52(1) (2019), 949–958] introduced the notions of AJ weak amenability and quotient ideal amenability for a Banach algebra A relative to a closed two-sided ideal J. They investigated the connection between the AJ -weak amenability of A and the weak amenability of AJ. However, their primary theorem relied on a flawed conclusion, and Theorem 2.13 in their work includes an incorrect result. In this paper, we present counterexamples to highlight these issues, then refine and establish their main theorem under less restrictive assumptions. Additionally, we provide alternative results and extend the analysis of these concepts to specific classes of Banach algebras, particularly triangular Banach algebras.

2020 Mathematics Subject Classification: Primary 46H10; Secondary 46H20; 46H25

Acknowledgement

We would like to sincerely thank the anonymous referees for their valuable feedback and constructive suggestions, which significantly improved the quality of this paper.

  1. (Communicated by Emanuel Chetcuti)

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Received: 2024-11-07
Accepted: 2025-01-16
Published Online: 2025-06-09
Published in Print: 2025-06-26

© 2025 Mathematical Institute Slovak Academy of Sciences

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