SOME GEOMETRIC PROPERTIES in ψ-DIRECT SUMS OF BANACH SPACES X ⊕ψ Y

A norm on C2 is said to be absolute if ‖(z, w) ‖ = ‖(|z|, |w|) ‖ and normalized if ‖(1, 0) ‖ = ‖(0, 1) ‖ = 1. In [2], they proved that the set Na of all absolute normalized norms on C2 corresponds to the family Ψ of all convex functions on [0, 1] satisfying that ψ(0) = ψ(1) = 1 and max{1 − t, t} ≤ ψ(t) ≤ 1 (0 ≤ t ≤ 1