Orthogonally additive holomorphic maps between C*-algebras

摘要

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, i.e., A = C-0 (X) and B = C-0 (Y), that there exist weight functions h(n) and a symbol map phi : Y -> X such that