scholarly journals The separable Jung constant in Banach spaces

2020 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Pier Luigi Papini
Keyword(s):  
Banach Spaces ◽  
Jung Constant

Diametrically Maximal and Constant Width Sets in Banach Spaces

2006 ◽  
Vol 58 (4) ◽  
pp. 820-842 ◽  
Author(s):  
J. P. Moreno ◽  
P. L. Papini ◽  
R. R. Phelps
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Hausdorff Space ◽  
Constant Width ◽  
Negative Answer ◽  
Empty Interior ◽  
Finite Dimensional ◽  
Jung Constant

AbstractWe characterize diametrically maximal and constant width sets inC(K), whereKis any compact Hausdorff space. These results are applied to prove that the sum of two diametrically maximal sets needs not be diametrically maximal, thus solving a question raised in a paper by Groemer. A characterization of diametrically maximal sets inis also given, providing a negative answer to Groemer's problem in finite dimensional spaces. We characterize constant width sets inc0(I), for everyI, and then we establish the connections between the Jung constant of a Banach space and the existence of constant width sets with empty interior. Porosity properties of families of sets of constant width and rotundity properties of diametrically maximal sets are also investigated. Finally, we present some results concerning non-reflexive and Hilbert spaces.

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