On the calculation of the James constant of Lorentz sequence spaces

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