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Convex functions on Banach spaces not containing $\ell_1$ |
Canad. Math. Bull. 40(1997), 10-18
Published:1997-03-01
Printed: Mar 1997
Printed: Mar 1997
- Jon Borwein
- Jon Vanderwerff
Abstract
There is a sizeable class of results precisely
relating boundedness, convergence and differentiability properties
of continuous convex functions on Banach spaces to whether or
not the space contains an isomorphic copy of $\ell_1$. In this
note, we provide constructions showing that the main such
results do not extend to natural broader classes of functions.
| MSC Classifications: |
46A55 - Convex sets in topological linear spaces; Choquet theory [See also 52A07] 46B20 - Geometry and structure of normed linear spaces 52A41 - Convex functions and convex programs [See also 26B25, 90C25] |