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 . 
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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
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