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- Title
Function Spaces and Nonsymmetric Norm Preserving Maps.
- Authors
Pazandeh, Hadis; Sady, Fereshteh
- Abstract
Let X,Y be compact Hausdorff spaces and A, B be either closed subspaces of C(X) and C(Y), respectively, containing constants or positive cones of such subspaces. In this paper we study surjections T : A → B satisfying the normcondition ∥T( f )T(g) -1∥Y = ∥ f g -1∥X for all f, g ϵ A, where ∥ · ∥X and ∥ · ∥Y denote the supremum norms. We show that under a mild condition on the strong boundary points of A and B (and the assumption T(i) = iT(1) in the subspace case), the map T is a weighted composition operator on the set of strong boundary points of B. This result is an improvement of the known results for uniformalgebra case to closed linear subspaces and their positive cones.
- Subjects
HAUSDORFF spaces; FUNCTION spaces; LINEAR operators; SUBSPACES (Mathematics); UNIFORM algebras
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2018, Vol 25, Issue 5, p729
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/bbms/1547780432