Vol. 60, No. 1, 1975

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A representation theorem for isometries of C(X,E)

Ka-Sing Lau

Vol. 60 (1975), No. 1, 229–233
Abstract

Let X, Y be compact Hausdorff spaces and let E, F be Banach spaces such that their duals are strictly convex. We show that a linear map T : C(X,E) C(Y,F) is an isometric isomorphism if and only if there exists a homeomorphism ϕ : Y X and a continuous map λ from Y to the set of isometric isomorphisms from E onto F (with the strong topology) such that Tf(y) = λ(y) f(ϕ(y)) for all y Y , f C(X,E).

Mathematical Subject Classification 2000
Primary: 46E40
Secondary: 47B37
Milestones
Received: 22 August 1974
Published: 1 September 1975
Authors
Ka-Sing Lau