Existence of a Lipschitz selection of the Chebyshev-centre map

Journal Article · Fri May 31 00:00:00 EDT 2013 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2013V204N05ABEH004315· OSTI ID:22122875

Druzhinin, Yuri Yu ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

The paper is concerned with the existence of a Lipschitz selection for the operator T{sub C} (the Chebyshev-centre map) that assigns to any bounded subset M of a Banach space X the set T{sub C}(M) of its Chebyshev centres. It is proved that if the unit sphere S(X) of X has an exposed smooth point, then T{sub C} does not have a Lipschitz selection. It is also proved that if X is finite dimensional the operator T{sub C} has a Lipschitz selection if and only if X is polyhedral. The operator T{sub C} is also shown to have a Lipschitz selection in the space c{sub 0}(K) and c-spaces. Bibliography: 4 titles.

• OSTI ID: 22122875
• Journal Information: Sbornik. Mathematics, Vol. 204, Issue 5; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BANACH SPACE
MAPS
MATHEMATICAL OPERATORS
SPHERES