## Abstract

Motivated by the systemic work of Lu [21, 23] we mainly consider the question of whether any Jordan higher derivation on some operator algebras is a higher derivation. Let A be a torsion free algebra over a commutative ring R, D be the set of all Jordan higher derivations D = {d_{n}} ^{∞}_{n=0} on A, and Δ be the set of all sequences {δ_{n}}^{∞}_{n=0} of Jordan derivations on A with δ_{0} = 0. Then there is a one to one correspondence between D and Δ. It is shown via this correspondence that every Jordan higher derivation on some operator algebras is a higher derivation. The involved operator algebras include CSL algebras, reexive algebras, nest algebras. At last, we describe local actions of Jordan higher derivations on nest algebras.

Original language | English |
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Pages (from-to) | 275-293 |

Number of pages | 19 |

Journal | Houston Journal of Mathematics |

Volume | 38 |

Issue number | 1 |

Publication status | Published - 2012 |

## Keywords

- CSL algebra
- Jordan higher derivation
- Nest algebra
- Reflexive algebra