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Non-squareness properties of Orlicz spaces equipped with the \(p\)-Amemiya norm. (English) Zbl 1247.46015

Summary: This paper is a continuation of the studies by Y. Cui et al. [Nonlinear Anal., Theory Methods Appl. 69, No. 5–6, A, 1796–1816 (2008; Zbl 1165.46005)] and Y. Cui et al. [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, A, 6343–6364 (2009; Zbl 1186.46015)]. Non-squareness, uniform non-squareness, locally uniform non-squareness of Orlicz spaces equipped with the \(p\)-Amemiya norm are studied. Criteria for these three properties in the Orlicz spaces \(L_{\varPhi ,p}\) are given in the most general case of an Orlicz function \(\varPhi \) and for all \(1\leq p\leq \infty \).

MSC:

46B20 Geometry and structure of normed linear spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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