A class of spaces with weak normal structure

Publisher： Cambridge University Press

E-ISSN： 1755-1633|49|3|523-528

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.49, Iss.3, 1994-06, pp. : 523-528

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Abstract

It has recently been shown that a Banach space enjoys the weak fixed point property if it is ε0-inquadrate for some ε0 < 2 and has WORTH; that is, if then, ║xn — x║ — ║xn + x║ → 0, for all x. We establish the stronger conclusion of weak normal structure under the substantially weaker assumption that the space has WORTH and is ‘ε0-inquadrate in every direction’ for some ε0 < 2.

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