(I)-envelopes of unit balls and James' characterization of reflexivity

• Autorzy: Ondřej F. K. Kalenda
• Języki publikacji: EN

Abstrakty

EN

We study the (I)-envelopes of the unit balls of Banach spaces. We show, in particular, that any nonreflexive space can be renormed in such a way that the (I)-envelope of the unit ball is not the whole bidual unit ball. Further, we give a simpler proof of James' characterization of reflexivity in the nonseparable case. We also study the spaces in which the (I)-envelope of the unit ball adds nothing.

Kategorie tematyczne

• 46A55: Convex sets in topological linear spaces; Choquet theory
• 46B10: Duality and reflexivity
• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 182
• Numer: 1
• Strony: 29-40

Daty

wydano

2007

Twórcy

autor

Ondřej F. K. Kalenda

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/sm182-1-2