Geodesic
Diameter 2 properties and convexity
Trond Arnold Abrahamsen1 ; Petr Hájek2 ; Olav Nygaard3 ; Jarno Talponen4 ; Stanimir Troyanski5
1Department of Mathematics University of Agder Postbox 422 4604 Kristiansand, Norway
2Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic and Department of Mathematics Faculty of Electrical Engineering Czech Technical University in Prague Zikova 4 160 00 Praha, Czech Republic
3Department of Mathematics University of Agder Postbox 422, 4604 Kristiansand, Norway
4Department of Physics and Mathematics University of Eastern Finland Box 111 FI-80101 Joensuu, Finland
5Departamento de Matemáticas Universidad de Murcia Campus de Espinardo 30100 Espinardo (Murcia), Spain and Institute of Mathematics and Informatics Bulgarian Academy of Sciences bl. 8, acad. G. Bonchev St. 1113 Sofia, Bulgaria
Studia Mathematica, Tome 232 (2016) no. 3, pp. 227-242
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We present an equivalent midpoint locally uniformly rotund (MLUR) renorming of $C[0,1]$ with the diameter 2 property (D2P), i.e. every non-empty relatively weakly open subset of the unit ball has diameter 2. An example of an MLUR space with the D2P and with convex combinations of slices of arbitrarily small diameter is also given.
DOI : 10.4064/sm8317-4-2016
Keywords: present equivalent midpoint locally uniformly rotund mlur renorming diameter property every non empty relatively weakly subset unit ball has diameter example mlur space with convex combinations slices arbitrarily small diameter given

Trond Arnold Abrahamsen  1   ; Petr Hájek  2   ; Olav Nygaard  3   ; Jarno Talponen  4   ; Stanimir Troyanski  5

1 Department of Mathematics University of Agder Postbox 422 4604 Kristiansand, Norway
2 Mathematical Institute Czech Academy of Sciences Žitná 25 115 67 Praha 1, Czech Republic and Department of Mathematics Faculty of Electrical Engineering Czech Technical University in Prague Zikova 4 160 00 Praha, Czech Republic
3 Department of Mathematics University of Agder Postbox 422, 4604 Kristiansand, Norway
4 Department of Physics and Mathematics University of Eastern Finland Box 111 FI-80101 Joensuu, Finland
5 Departamento de Matemáticas Universidad de Murcia Campus de Espinardo 30100 Espinardo (Murcia), Spain and Institute of Mathematics and Informatics Bulgarian Academy of Sciences bl. 8, acad. G. Bonchev St. 1113 Sofia, Bulgaria 
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Trond Arnold Abrahamsen; Petr Hájek; Olav Nygaard; Jarno Talponen; Stanimir Troyanski. Diameter 2 properties and convexity. Studia Mathematica, Tome 232 (2016) no. 3, pp. 227-242. doi: 10.4064/sm8317-4-2016

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