On the calculation of the James constant of Lorentz sequence spaces

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Abstract

In [M. Kato and L. Maligranda, On James and Jordan-von Neumannconstants of Lorentz sequence spaces, J. Math. Anal. Appl., 258(2001), 457–465], theJames constant of the 2-dimensional Lorentz sequence space d(2)(!; q) is computed inthe case where 2 · q < 1. It is an open problem to compute it in the case where1 · q < 2. In this paper, we completely determine the James constant of d(2)(!; q) inthe case where 1 · q < 2.

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