# Orthogonally additive polynomials on Fourier algebras

@article{Alaminos2015OrthogonallyAP,
title={Orthogonally additive polynomials on Fourier algebras},
author={Jer{\'o}nimo Alaminos and J. Extremera and A. R. Villena},
journal={Journal of Mathematical Analysis and Applications},
year={2015},
volume={422},
pages={72-83}
}
• Published 1 February 2015
• Mathematics
• Journal of Mathematical Analysis and Applications
7 Citations
Orthogonally additive polynomials on the algebras of approximable operators
• Mathematics
• 2018
Abstract Let X and Y be Banach spaces, let stands for the algebra of approximable operators on X, and let be an orthogonally additive, continuous n-homogeneous polynomial. If has the bounded
Orthogonally Additive Polynomials and Orthosymmetric Maps in Banach Algebras with Properties 𝔸 and 𝔹
• Mathematics
Proceedings of the Edinburgh Mathematical Society
• 2015
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;
Orthogonally additive polynomials on convolution algebras associated with a compact group
• Mathematics
Journal of Mathematical Analysis and Applications
• 2019
Orthogonally additive polynomials on non-commutative $$L^p$$-spaces
• Mathematics
Revista Matemática Complutense
• 2019
Let $\mathcal{M}$ be a von Neumann algebra with a normal semifinite faithful trace $\tau$. We prove that every continuous $m$-homogeneous polynomial $P$ from $L^p(\mathcal{M},\tau)$, with

## References

SHOWING 1-10 OF 23 REFERENCES
• Mathematics
• 2007
We show that for every orthogonally additive scalar n-homogeneous polynomial P on a C*-algebra A there exists phi in A* satisfying P(x) = phi(x(n)), for each element x in A. The vector-valued
Cohomology and the operator space structure of the Fourier algebra and its second dual
• Mathematics
• 2001
Let G be a locally compact group. We introduce the notion of operator weak amenability for a completely contractive Banach algebra. We then study the potential operator weak amenability of the
Orthogonally Additive Polynomials over C(K) are Measures—A Short Proof
• Mathematics
• 2006
Abstract.We give a simple proof of the fact that orthogonally additive polynomials on C(K) are represented by regular Borel measures over K. We also prove that the Aron-Berner extension preserves
Homogeneous Orthogonally Additive Polynomials on Banach Lattices
• Mathematics
• 2006
The main result in this paper is a representation theorem for homogeneous orthogonally additive polynomials on Banach lattices. The representation theorem is used to study the linear span of the set
A representation theorem for orthogonally additive polynomials on Riesz spaces
• Mathematics
• 2012