Bilinear isometries on subspaces of continuous functions
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Title
Bilinear isometries on subspaces of continuous functionsDate
2010-03-18Publisher
Wiley-VCH VerlagISSN
0025-584X; 1522-2616Bibliographic citation
Mathematische Nachrichten (2010) vol. 283, no. 4, p. 568–572Type
info:eu-repo/semantics/articlePublisher version
http://onlinelibrary.wiley.com/doi/10.1002/mana.200610836/abstractVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
Let A and B be strongly separating linear subspaces of C0(X) and C0(Y ), respectively, and assume that ∂A ̸= ∅ (∂A stands for the set of generalized peak points for A) and ∂B ≠ ∅. Let T : A×B −→ C0(Z) be a bilinear ... [+]
Let A and B be strongly separating linear subspaces of C0(X) and C0(Y ), respectively, and assume that ∂A ̸= ∅ (∂A stands for the set of generalized peak points for A) and ∂B ≠ ∅. Let T : A×B −→ C0(Z) be a bilinear isometry. Then there exist a nonempty subset Z0 of Z, a surjective continuous mapping h : Z0 −→ ∂A × ∂B and a norm-one continuous function a : Z0 −→ K such that T(f,g)(z) = a(z)f(πx(h(z))g(πy(h(z)) for all z ∈ Z0 and every pair (f, g) ∈ A × B. These results can be applied, for example, to non-unital function algebras. [-]
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