Bilinear isometries on spaces of vector-valued continuous functions
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Títol
Bilinear isometries on spaces of vector-valued continuous functionsData de publicació
2012Editor
ElsevierISSN
0022-247XTipus de document
info:eu-repo/semantics/articleVersió de l'editorial
http://www.sciencedirect.com/science/article/pii/S0022247X11006020Versió
info:eu-repo/semantics/acceptedVersionParaules clau / Matèries
Resum
Let X, Y, Z be compact Hausdorff spaces and let E1, E2, E3 be Banach spaces. If T:C(X,E1)×C(Y,E2)→C(Z,E3) is a bilinear isometry which is stable on constants and E3 is strictly convex, then there exist a nonempty ... [+]
Let X, Y, Z be compact Hausdorff spaces and let E1, E2, E3 be Banach spaces. If T:C(X,E1)×C(Y,E2)→C(Z,E3) is a bilinear isometry which is stable on constants and E3 is strictly convex, then there exist a nonempty subset Z0 of Z, a surjective continuous mapping h:Z0→X×Y and a continuous function ω:Z0→Bil(E1×E2,E3) such that
T(f,g)(z)=ω(z)(f(πX(h(z))),g(πY(h(z))))
for all z∈Z0 and every pair (f,g)∈C(X,E1)×C(Y,E2). This result generalizes the main theorems in Cambern (1978) [2] and Moreno and Rodríguez (2005) [7]. [-]
Publicat a
Journal of Mathametical Analysis and Applications, 385, 1Drets d'accés
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