Taiwanese Journal of Mathematics

HAUSDORFF NORMS OF RETRACTIONS IN BANACH SPACES OF CONTINUOUS FUNCTIONS

Vittorio Colao, Alessandro Trombetta, and Giulio Trombetta

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Abstract

We construct retractions with positive lower Hausdorff norms and small Hausdorff norms in Banach spaces of real continuous functions which domains are not necessarily bounded or finite dimensional. Moreover, we give precise formulas for the lower Hausdorff norms and the Hausdorff norms of such maps.

Article information

Source
Taiwanese J. Math., Volume 13, Number 4 (2009), 1139-1158.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405497

Digital Object Identifier
doi:10.11650/twjm/1500405497

Mathematical Reviews number (MathSciNet)
MR2543732

Zentralblatt MATH identifier
1186.46025

Subjects
Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions 46B20: Geometry and structure of normed linear spaces 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

Keywords
Hausdorff measure of noncompactness lower Hausdorff norm Hausdorff norm retraction Hilbert cube

Citation

Colao, Vittorio; Trombetta, Alessandro; Trombetta, Giulio. HAUSDORFF NORMS OF RETRACTIONS IN BANACH SPACES OF CONTINUOUS FUNCTIONS. Taiwanese J. Math. 13 (2009), no. 4, 1139--1158. doi:10.11650/twjm/1500405497. https://projecteuclid.org/euclid.twjm/1500405497


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