- Title
- Convex functions on Banach spaces not containing ℓ1
- Creator
- Borwein, Jon; Vanderwerff, Jon
- Relation
- Canadian Mathematical Bulletin Vol. 40, Issue 1, p. 10-18
- Publisher Link
- http://dx.doi.org/10.4153/CMB-1997-002-1
- Publisher
- University of Toronto Press
- Resource Type
- journal article
- Date
- 1997
- Description
- 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 ℓ1. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.
- Subject
- convex functions; Banach spaces; differentiability properties; boundedness; convergence
- Identifier
- http://hdl.handle.net/1959.13/1046795
- Identifier
- uon:14688
- Identifier
- ISSN:0008-4395
- Language
- eng
- Reviewed
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