## Abstract

This paper considers Banach algebras with properties A or B, introduced recently by Alaminos et al. The class of Banach algebras satisfying either of these two properties is quite large; in particular, it includes C ∗-algebras and group algebras on locally compact groups. Our first main result states that a continuous orthogonally additive n-homogeneous polynomial on a commutative Banach algebra with property and having a bounded approximate identity is of a standard form. The other main results describe Banach algebras A with property and having a bounded approximate identity that admit non-zero continuous symmetric orthosymmetric n-linear maps from A^{n} into C.

Original language | English |
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Pages (from-to) | 559-568 |

Number of pages | 10 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 59 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2016 |

## Keywords

- 2010 Mathematics subject classification: Primary 43A20
- 46H05
- 46J05
- 47B48