2015/12/24 by Qingying Bu, Bu, Qingying, Ming-Hsiu Hsu +3
Mathematics · #17C65 #46G25 #46L05 #47B33 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:17C65 #msc:46G25 #msc:46L05 #msc:47B33
paper · pdf · doi:10.48550/arxiv.1512.07714
23 pages, 1st draft 2013.8.9, this version 2015.3.20
arxiv created 2015/12/24 · arxiv updated 2015/12/25
Let A,B be C*-algebras, BA(0;r) the open ball in A centered at 0 with radius r>0, and H:BA(0;r)→ B an orthogonally additive holomorphic map. If H is zero product preserving on positive elements in BA(0;r), we show, in the commutative case when A=C0(X) and B=C0(Y), that there exist weight functions hn's and a symbol map φ: Y→ X such that H(f)=∑n≥1 hn (f∘φ)n, ∀ f∈ BC0(X)(0;r). In the general case, we show that if H is also conformal then there exist central multipliers hn's of B and a surjective Jordan isomorphism J: A→ B such that H(a) = ∑n≥1 hn J(a)n, ∀ a∈ BA(0;r). If, in addition, H is zero product preserving on the whole BA(0;r), then J is an algebra isomorphism. %Similar conclusions hold for orthogonally additive n-homogeneous polynomials which are n-isometries.