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arXiv · 1802.00239

Orthogonally additive polynomials on convolution algebras associated with a compact group

J. Alaminos·J. Extremera·M. L. C. Godoy·A. R. Villena
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Abstract

Let $G$ be a compact group, let $X$ be a Banach space, and let $P\colon L^1(G)\to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $\Phi\colon L^1(G)\to X$ such that $P(f)=\Phi \bigl(f\ast\stackrel{n}{\cdots}\ast f \bigr)$ for each $f\in L^1(G)$. We also seek analogues of this result about $L^1(G)$ for various other convolution algebras, including $L^p(G)$, for $1< p\le\infty$, and $C(G)$.

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J. Alaminos, J. Extremera, M. L. C. Godoy, A. R. Villena. 2018-02-01. Orthogonally additive polynomials on convolution algebras associated with a compact group. https://arxiv.org/abs/1802.00239

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