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Orthogonally Additive Polynomials and Orthosymmetric Maps in Banach Algebras with Properties A and BAlaminos, J; Bresar, M; Spenko, S; Villena, A R
Proceedings of the Edinburgh Mathematical Society, 08/2016, Volume: 59, Issue: 3Journal Article
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 super(*)-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 A and having a bounded approximate identity is of a standard form. The other main results describe Banach algebras A with property B and having a bounded approximate identity that admit non-zero continuous symmetric orthosymmetric n-linear maps from A super(n)into C.
