Existence of a Lipschitz selection of the Chebyshev-centre map
Yuri Yurievich Druzhinin · Sbornik Mathematics · 2013
The paper is concerned with the existence of a Lipschitz selection for the operator (the Chebyshev-centre map) that assigns to any bounded subset of a Banach space the set of its Chebyshev centres. It is proved that if the unit sphere of has an exposed smooth point, then does not have a Lipschitz selection. It is also proved that if is finite dimensional the operator has a Lipschitz selection if and only if is polyhedral. The operator is also shown to have a Lipschitz selection in the space and -spaces. Bibliography: 4 titles.