Abstract
We give criteria for local uniform non-squareness of Orlicz–Lorentz function spaces varLambda _{varphi ,omega } equipped with the Luxemburg norm, where the widest possible class of convex Orlicz functions is admitted. As immediate consequences, criteria for local uniform non-squareness of Orlicz function spaces L^{varphi }, which complete the already known results, are deduced.
Highlights
We say that a Banach space X is non-square if for any x and y from S(X )
Recall that uniform non-squareness of Banach spaces was defined by James as a geometric property which implies super-reflexivity
Recall that the Köthe space E is called a symmetric space if E is rearrangement invariant in the sense that if x ∈ E, y ∈ L0 and x∗ = y∗, y ∈ E and x = y
Summary
We say that a Banach space X is non-square if for any x and y from S(X ) A Banach space X is said exists δ = δ(x) ∈ (0, 1) such to be locally uniformly that min( We say that a Banach space X is uniformly non-square if there exists δ ∈ (0, 1) such that min(
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