Orthogonally Additive Polynomials and Orthosymmetric Maps in Banach Algebras with Properties A and B

J. Alaminos, M. Brešar, Spela Spenko, A. R. Villena

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 An into C.

Original languageEnglish
Pages (from-to)559-568
Number of pages10
JournalProceedings of the Edinburgh Mathematical Society
Volume59
Issue number3
DOIs
Publication statusPublished - 2016

Keywords

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

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