Dual of two dimensional Lorentz sequence spaces

In [M. Kato and L. Maligranda, On James and Jordan–von Neumann constants of Lorentz sequence spaces, J. Math. Anal. Appl. 258 (2001) 457–465], it is an open problem to compute the James constant of the dual space of two dimensional Lorentz sequence space d(2)(w,q)d(2)(w,q). In this paper, we shall determine the dual norm of d(2)(w,q)d(2)(w,q) and completely compute the James constant of d(2)(w,q)d(2)(w,q).