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Formulae for nonsquare constants of Orlicz sequence spaces with Orlicz norm

Yan Y.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 3

233-246

Let l^phi be the Orlicz Sequence space generated by a N-function Phi(u) equipped with the Orlicz norm, phi be the right derivative of Phi. We show that the nonsquare constants Cj (l^phi] in the sense of James and Cj (l^phi ) in the sense of Schaffer satisfy: (i) if phi is concave, then Cj(l^phi) = sup inf [...], (ii) if phi is convex, then Cs(l^phi) = inf inf [...]. With this result we obtain some formulae for practical computation of non-square constants.