Non-squareness properties of Orlicz–Lorentz sequence spaces

In this paper criteria for non-squareness properties (non-squareness, local uniform non-squareness and uniform non-squareness) of Orlicz–Lorentz sequence spaces λϕ,ω and of their n-dimensional subspaces λn ϕ,ω (n 2) as well as of the subspaces (λϕ,ω)a of all order continuous elements in λϕ,ω are given. Since degenerate Orlicz functions ϕ and degenerate weight sequences ω are also admitted, these investigations concern the most possible wide class of Orlicz–Lorentz sequence spaces. Finally, as immediate consequences, criteria for all non-squareness properties of Orlicz sequence spaces, which complete the results of Sundaresan (1966) [53], Hudzik (1985) [23], Hudzik (1985) [24], are deduced. It is worth recalling that uniform non-squareness is an important property, because it implies super-reflexivity as well as the fixed point property (see James (1964) [31], James (1972) [33] and García-Falset et al. (2006) [19]). © 2012 Elsevier Inc. All rights reserved.