Local higher derivations on Hilbert C*-modules

Document Type : Original Paper

Author

Department of Mathematics, Payame Noor University, P.O. Box 19395­3697, Tehran, Iran.

Abstract

‎A sequence of continuous linear mappings $\{\Phi_n\}_{n=0}^\infty$ form a Hilbert C* -‎module‎ M into M is called a local higher derivation if for each $a\in\mathfrak{M}$ there is a continuous higher derivation $\{\varphi_{a,n}\}_{n=0}^\infty$ ‎on‎ M such that $\Phi_n(a)=\varphi_{a,n}(a)$ for each non-negative integer n‎. ‎In this paper w‎e show that if M is a Hilbert C* -‎module‎ such that every local derivation on M is a derivation, then each local higher derivation on M‎ is a higher derivation‎. Also, we prove that each local higher derivation on a unital C*-algebra is automatically continuous‎.

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References

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Journal of Advanced Mathematical Modeling
Volume 13, Issue 4 - Serial Number 32
February 2024
Pages 524-533

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History

  • Receive Date: 27 July 2023
  • Revise Date: 29 November 2023
  • Accept Date: 23 January 2024

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