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Convex functions on Banach spaces not containing $ l_1$

Borwein, Jonathan M. and Vanderwerff, Jon D. (1997) Convex functions on Banach spaces not containing $ l_1$. Canad. Math. Bull., 40 (1). pp. 10-18.

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    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 ‡1. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.

    Item Type: Article
    Subjects: 46-xx Functional analysis > 46Axx Topological linear spaces and related structures
    46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
    52-xx Convex and discrete geometry > 52Axx General convexity
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 13 Jan 2015 17:07
    Last Modified: 13 Jan 2015 17:07
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1532

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