Orthogonally additive polynomials on the algebras of approximable operators
Orthogonally additive polynomials on the algebras of approximable operators
Let X and Y be Banach spaces, let A(X) stands for the algebra of approximable operators on X, and let P:A(X)→Y be an orthogonally additive, continuous n-homogeneous polynomial. If X∗ has the bounded approximation property, then we show that there exists a unique continuous linear map Φ:A(X)→Y such that P(T)=Φ(Tn) …