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On the Banach-Stone problem

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Jeang J.-S., Wong N.-C.

Studia Mathematica

2003

tom 155

nr 2

95-105

Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of $ℓ₂^{∞}$ then T can be written as a weighted composition operator in the classical sense.

Ograniczanie wyników

1 Studia Mathematica

1 Jeang J.-S.

1 Wong N.-C.

1 2003

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On the Banach-Stone problem