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Bilinear isometries on subspaces of continuous functions

✍ Scribed by Juan J. Font; M. Sanchis

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 99 KB
Volume: 283
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200610836

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✦ Synopsis

Bilinear isometry, subspaces of continuous functions, generalized peak point

MSC (2000) 46A55, 46E15

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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