|
|
|
|
|
Small isomorphisms of
C(X,E) spaces
Krzysztof Jarosz |
|
Vol. 138 (1989), No. 2, 295–315
|
Abstract |
|
A linear map T between two Banach spaces A and B is called 𝜖-isometry if (1 − 𝜖)∥f∥≤∥Tf∥≤ (1 + 𝜖)∥f∥, for any f ∈ A. In the paper we investigate injective and surjective 𝜖-isometries between Banach spaces of continuous E-valued functions. We prove that, under some geometrical assumptions on the Banach space E, any such 𝜖-isometry is induced by a continuous function between the corresponding compact Hausdorff spaces. We discuss also the question whether such an 𝜖-isometry has to be just a small perturbation of an isometry. |
Mathematical Subject Classification 2000
Primary: 46E40
Secondary: 46B20
|
Milestones
Received: 15 December 1987
Revised: 26 April 1988
Published: 1 June 1989
|
Authors |
| Krzysztof Jarosz | |
|
