Orthogonally additive holomorphic maps between C$^{*}$-algebras

Abstract

Let A, B be C*-algebras, B A (0; r) the open ball in A centered at 0 with radius r > 0, and H : B A (0; r) → B an orthogonally additive holomorphic map. If H is zero product preserving on positive elements in B A (0; r), we show, in the commutative case when A = C 0 (X) and B = C 0 (Y ), that there exist weight functions h n 's and a symbol map ϕ : Y → X such thatIn the general case, we show that if H is also conformal then there exist central multipliers h n 's of B and a surjective Jordan isomorphism J : A → B such thatIf, in addition, H is zero product preserving on the whole B A (0; r), then J is an algebra isomorphism.