Diameter 2 properties and convexity

• Autorzy: Trond Arnold Abrahamsen , Petr Hájek , Olav Nygaard , Jarno Talponen , Stanimir Troyanski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 232
• Numer: 3
• Strony: 227-242

Daty

wydano

2016

Twórcy

autor

Trond Arnold Abrahamsen

• Department of Mathematics, University of Agder, Postbox 422, 4604 Kristiansand, Norway

autor

Petr Hájek

• Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
• Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Zikova 4, 160 00 Praha, Czech Republic

autor

Olav Nygaard

• Department of Mathematics, University of Agder, Postbox 422, 4604 Kristiansand, Norway

autor

Jarno Talponen

• Department of Physics and Mathematics, University of Eastern Finland, Box 111, FI-80101 Joensuu, Finland

autor

Stanimir Troyanski

• Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo (Murcia), Spain
• Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, bl. 8, acad. G. Bonchev St., 1113 Sofia, Bulgaria

Identyfikatory

DOI

10.4064/sm8317-4-2016