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arXiv · 1802.00238

Orthogonally additive polynomials on the algebras of approximable operators

J. Alaminos·M. L. C. Godoy·A. R. Villena
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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 $T\in\mathcal{A}(X)$.

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J. Alaminos, M. L. C. Godoy, A. R. Villena. 2018-02-01. Orthogonally additive polynomials on the algebras of approximable operators. https://doi.org/10.1080/03081087.2018.1476445

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