# 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} }

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

- MathematicsRevista 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 11 REFERENCES

Orthogonally additive polynomials on C*-Algebras

- 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 polynomials on Fourier algebras

- Mathematics
- 2015

Abstract We show that an n-homogeneous polynomial P on the Fourier algebra A ( G ) of a locally compact group G can be represented in the form P ( f ) = 〈 T , f n 〉 ( f ∈ A ( G ) ) for some T in the…

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

- MathematicsProceedings 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 Banach function algebras

- Mathematics
- 2017

Abstract For a Banach function algebra A, we consider the problem of representing a continuous d-homogeneous polynomial P : A → X , where X is an arbitrary Banach space, that satisfies the property P…

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

- Mathematics
- 2000

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