Orthogonally additive polynomials on the algebras of approximable operators
Abstract
Let $X$ and $Y$ be Banach spaces, let $\mathcal{A}(X)$ stands for the algebra of approximable operators on $X$, and let $P\colon\mathcal{A}(X)\to Y$ be an orthogonally additive, continuous $n$homogeneous polynomial. If $X^*$ has the bounded approximation property, then we show that there exists a unique continuous linear map $\Phi\colon\mathcal{A}(X)\to Y$ such that $P(T)=\Phi(T^n)$ for each $T\in\mathcal{A}(X)$.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.00238
 Bibcode:
 2018arXiv180200238A
 Keywords:

 Mathematics  Functional Analysis;
 47H60;
 46H35;
 47L10
 EPrint:
 To appear in Linear and Multilinear Algebra