### Abstract

Let A be a semisimple Danach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Danach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation expansion formula on zero products.

Original language | English |
---|---|

Pages (from-to) | 193-202 |

Number of pages | 10 |

Journal | Studia Mathematica |

Volume | 190 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 Mar 18 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Partially defined σ-derivations on semisimple Banach algebras'. Together they form a unique fingerprint.

## Cite this

Lee, T. K., & Liu, C. K. (2009). Partially defined σ-derivations on semisimple Banach algebras.

*Studia Mathematica*,*190*(2), 193-202. https://doi.org/10.4064/sm190-2-7