Metrical characterization of super-reflexivity and linear type of Banach spaces
β Scribed by Florent Baudier
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 164 KB
- Volume
- 89
- Category
- Article
- ISSN
- 0003-889X
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π SIMILAR VOLUMES
Let X be a Banach space with a basis. We prove the following characterizations: (i) X is finite-dimensional if and only if every power-bounded operator is uniformly ergodic. (ii) X is reflexive if and only if every power-bounded operator is mean ergodic. (iii) X is quasi-reflexive of order one if
Here Z denotes the dual of Z, and β³# denotes the polar of β³ taken in Z.
A function defined on a Banach space X is called D-convex if it can be represented as a difference of two continuous convex functions. In this work we study the relationship between some geometrical properties of a Banach space X and the behaviour of the class of all D-convex functions defined on it
## A Metric Characterization of Normed Linear Spaces By SIEGFRIED GAHLER of Berlin and GRATTAN MURPHY\*) of Orono (Eingegangen am 18.12. 1980) \*) The research in this paper was carried out while the second author was a visitor at the Akademie der Wissenschaften der DDR under an exchange agreement