# Orthogonally additive polynomials on C*-Algebras

@article{Palazuelos2007OrthogonallyAP, title={Orthogonally additive polynomials on C*-Algebras}, author={Carlos Palazuelos and Antonio M. Peralta and Ignacio Villanueva}, journal={Quarterly Journal of Mathematics}, year={2007}, volume={59}, pages={363-374} }

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 analogue follows as a corollary.

## 26 Citations

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We study the space of orthogonally additive $n$-homogeneous polynomials on $C(K)$. There are two natural norms on this space. First, there is the usual supremum norm of uniform convergence on the…

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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,…

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Let E be a Banach lattice, λ1, λ2, . . . , λk non-zero scalars and φ1, φ2, . . . , φk pairwise independent linear functionals on E. We show that if k < m then ∑k j=1 λjφ m j is orthogonally additive…

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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,…

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