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- Title
Generalized norm preserving maps between subsets of continuous functions.
- Authors
Jafarzadeh, Bagher; Sady, Fereshteh
- Abstract
Let X and Y be locally compact Hausdorff spaces. In this paper we study surjections T:A⟶B between certain subsets A and B of C0(X) and C0(Y), respectively, satisfying the norm condition ‖φ(Tf,Tg)‖Y=‖φ(f,g)‖X, f,g∈A, for some continuous function φ:C×C⟶R+. Here ‖·‖X and ‖·‖Y denote the supremum norms on C0(X) and C0(Y), respectively. We show that if A and B are (positive parts of) subspaces or multiplicative subsets, then T is a composition operator (in modulus) inducing a homeomorphism between strong boundary points of A and B. Our results generalize the recent results concerning multiplicatively norm preserving maps, as well as, norm additive in modulus maps between function algebras to more general cases.
- Subjects
CONTINUOUS functions; HAUSDORFF spaces; SUBSPACES (Mathematics); COMPOSITION operators; HOMEOMORPHISMS
- Publication
Positivity, 2019, Vol 23, Issue 1, p111
- ISSN
1385-1292
- Publication type
Article
- DOI
10.1007/s11117-018-0597-y