# Orthogonally additive polynomials on the algebras of approximable operators

@article{Alaminos2018OrthogonallyAP,
title={Orthogonally additive polynomials on the algebras of approximable operators},
author={Jer{\'o}nimo Alaminos and M. L. C. Godoy and A. R. Villena},
journal={Linear and Multilinear Algebra},
year={2018},
volume={67},
pages={1922 - 1936}
}
• Published 1 February 2018
• Mathematics
• Linear and Multilinear Algebra
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 approximation property, then we show that there exists a unique continuous linear map such that for each .
2 Citations
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
Miscellany

## References

SHOWING 1-10 OF 11 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
Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
• Mathematics
• 2013
We study holomorphic maps between C-algebras and , when is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball . If we assume that is orthogonality
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 holomorphic functions on C^*-algebras
• Mathematics
• 2012
Let A be a C ∗ -algebra. We prove that a holomorphic function of bounded type f : A → C is orthogonally additive on Asa if, and only if, it is additive on elements having zeroproduct if, and only if,
Banach algebras and automatic continuity
Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination. This volume expounds the general theory of Banach algebras,
Banach algebras and automatic continuity. Vol. 24, London mathematical society monographs new series, New York (NY): Oxford Science Publications
• 2000
London mathematical society monographs new series
• Banach algebras and automatic continuity
• 2000
A(X)) ⊂ Y . Our final task is to prove the uniqueness of the map Φ. Suppose that Ψ : A(X) → Y is a continuous linear map such that P (T ) = Ψ(T n ) for each T ∈ A(X)
• Since F (X) is dense in A(X), Φ is continuous, and Y is closed in Y * * , it may be concluded that Φ