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A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund
Published online by Cambridge University Press: 20 November 2018
Abstract
A Banach space is fully 2-rotund if (xn) converges whenever ‖xn + xm‖ converges as m, n → ∞ and locally uniformly rotund if xn → x whenever ‖xn‖ and ‖(xn + x)/2‖ → ‖x‖.
We show that I2 with the equivalent norm
is fully 2-rotund but not locally uniformly rotund, thus answering in the negative a question first raised by Fan and Glicksberg in 1958.
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- Copyright © Canadian Mathematical Society 1983
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