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On the stability of bi-derivations in Banach algebras

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대한수학회 (The Korean Mathematical Society)|2011.09|대한수학회보 (Bulletin of the KMS)|제48권 제5호|pp. 959-967

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참고문헌

키워드

stabilitybi-derivationapproximate bi-derivation
주제분류수학

초록

Let A be a Banach algebra and let f:A×A→A be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f:A×A→A is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f=0.

Abstract

Let A be a Banach algebra and let f:A×A→A be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f:A×A→A is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f=0.

참고문헌 (19)

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