Erratum to: Surjective isometries on spaces of vector valued continuous and Lipschitz functions

Erratum to: Surjective isometries on spaces of vector valued continuous and Lipschitz functions Positivity (2016) 20:757–759 DOI 10.1007/s11117-016-0436-y Positivity ERRATUM Erratum to: Surjective isometries on spaces of vector valued continuous and Lipschitz functions Fernanda Botelho Published online: 4 August 2016 © Springer International Publishing 2016 Erratum to: Positivity (2013) 17:395–405 DOI 10.1007/s11117-012-0175-7 In the original article, the authors claimed incorrectly that the set of extreme points of the unit ball of a subspace A of C (X, F ) (X a compact Hausdorff space and F a ∗ ∗ Banach space) containing the constant functions is equal to {v ◦ δ : A → C,v ∈ ∗ ∗ ext (F ), x ∈ X }, ext (F ) denoting the set of extreme points of the unit ball of the 1 1 dual space F . We obtain the same conclusion but under some constrains on the range space and on A. More precisely, we assume that the range space is a reflexive Banach space with strictly convex dual and A separates X in the sense of Definition 3.1 in the original article. Strict convexity of the dual implies that F is smooth and then for ∗ ∗ ∗ every unit vector u ∈ F there exits a unique functional u ∈ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Erratum to: Surjective isometries on spaces of vector valued continuous and Lipschitz functions

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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-016-0436-y
Publisher site
See Article on Publisher Site

Abstract

Positivity (2016) 20:757–759 DOI 10.1007/s11117-016-0436-y Positivity ERRATUM Erratum to: Surjective isometries on spaces of vector valued continuous and Lipschitz functions Fernanda Botelho Published online: 4 August 2016 © Springer International Publishing 2016 Erratum to: Positivity (2013) 17:395–405 DOI 10.1007/s11117-012-0175-7 In the original article, the authors claimed incorrectly that the set of extreme points of the unit ball of a subspace A of C (X, F ) (X a compact Hausdorff space and F a ∗ ∗ Banach space) containing the constant functions is equal to {v ◦ δ : A → C,v ∈ ∗ ∗ ext (F ), x ∈ X }, ext (F ) denoting the set of extreme points of the unit ball of the 1 1 dual space F . We obtain the same conclusion but under some constrains on the range space and on A. More precisely, we assume that the range space is a reflexive Banach space with strictly convex dual and A separates X in the sense of Definition 3.1 in the original article. Strict convexity of the dual implies that F is smooth and then for ∗ ∗ ∗ every unit vector u ∈ F there exits a unique functional u ∈

Journal

PositivitySpringer Journals

Published: Aug 4, 2016

References

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