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<p>Bourgin (Duke Math J 16:385–397, 1949) proved that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is automatically a ring homomorphism. Martindale (Proc Am Math Soc 21:695–698, 1969) proved that every multiplicative isomorphism from a prime ring containing a nontrivial idempotent onto an arbitrary ring is automatically additive. We show these results for approximate multiplicative skew derivations and approximate skew derivations. Some closely related results are also discussed. Furthermore, we give some important consequences and illustrative examples from our main results.</p>

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On approximately skew derivations

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • Hamid Khodaei,
  • Mehdi Rostami,
  • Ahmad Alinejad

摘要

Bourgin (Duke Math J 16:385–397, 1949) proved that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is automatically a ring homomorphism. Martindale (Proc Am Math Soc 21:695–698, 1969) proved that every multiplicative isomorphism from a prime ring containing a nontrivial idempotent onto an arbitrary ring is automatically additive. We show these results for approximate multiplicative skew derivations and approximate skew derivations. Some closely related results are also discussed. Furthermore, we give some important consequences and illustrative examples from our main results.