## Abstract

This paper is devoted to local derivations on subalgebras on the algebra S(M, τ) of all τ-measurable operators affiliated with a von Neumann algebra M without abelian summands and with a faithful normal semi-finite trace τ. We prove that if A is a solid *-subalgebra in S(M, τ) such that p∈A for all projection p ∈ M with finite trace, then every local derivation on the algebra A is a derivation. This result is new even in the case of standard subalgebras on the algebra B(H) of all bounded linear operators on a Hilbert space H. We also apply our main theorem to the algebra S_{0}(M, τ) of all τ-compact operators affiliated with a semi-finite von Neumann algebra M and with a faithful normal semi-finite trace τ.

Original language | English |
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Pages (from-to) | 1009-1017 |

Number of pages | 9 |

Journal | Mediterranean Journal of Mathematics |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 8 2015 |

Externally published | Yes |

## Keywords

- Derivation
- local derivation
- measurable operator
- τ-compact operator

## ASJC Scopus subject areas

- Mathematics(all)