Points of nonsquareness of Lorentz spaces 
                
                  
                    
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Kolwicz, Paweł; Panfil, Agata

doi:10.1186/1029-242x-2014-467

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…Recall that space X is called non-square [23], if for every x, y ∈ S X , min{ x + y , x − y } < 2. Now, we discuss the relationship between δ a X ( ) and non-squareness.…”

Section: Introductionmentioning

confidence: 99%

Some Moduli of Angles in Banach Spaces

Du¹,

Ahmad²,

Din³

et al. 2022

Mathematics

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In this paper, we mainly discuss the angle modulus of convexity δXa(ϵ) and the angle modulus of smoothness ρXa(ϵ) in a real normed linear space X, which are closely related to the classical modulus of convexity δX(ϵ) and the modulus of smoothness ρX(ϵ). Some geometric properties of the two moduli were investigated. In particular, we obtained a characterization of uniform non-squareness in terms of ρXa(1). Meanwhile, we studied the relationships between δXa(ϵ), ρXa(ϵ) and other geometric constants of real normed linear spaces through some equalities and inequalities. Moreover, these two coefficients were computed for some concrete spaces.

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“…Recall that space X is called non-square [23], if for every x, y ∈ S X , min{ x + y , x − y } < 2. Now, we discuss the relationship between δ a X ( ) and non-squareness.…”

Section: Introductionmentioning

confidence: 99%

Some Moduli of Angles in Banach Spaces

Du¹,

Ahmad²,

Din³

et al. 2022

Mathematics

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show abstract

“…A point x ∈ S(X) is called uniformly non-ℓ 2 1 (or uniformly non-square), if there exists δ > 0 such that min( x + y , x − y ) < 2 − δ for all y ∈ S(X). It is worth to mention that non-square points and non-squareness properties of the above type have been considered in context of many spaces [8,13,14,21,22]. Proposition 4.4.…”

Section: The Daugavet Property In the Musielak-orlicz Spacesmentioning

confidence: 99%

The Daugavet property in the Musielak–Orlicz spaces

Kamińska

Kubiak

2015

Journal of Mathematical Analysis and Applications

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Abstract. We show that among all Musielak-Orlicz function spaces on a σ-finite non-atomic complete measure space equipped with either the Luxemburg norm or the Orlicz norm the only spaces with the Daugavet property are L1, L∞, L1 ⊕1 L∞ and L1 ⊕∞ L∞. In particular, we obtain complete characterizations of the Daugavet property in the weighted interpolation spaces, the variable exponent Lebesgue spaces (Nakano spaces) and the Orlicz spaces.

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“…However, the studies of global properties are not always sufficient. The geometric structure of a separated point of a Banach space (Banach lattice) has been intensively investigated recently (see [7,8,14,15,19,24,25,27,28]). On the other hand, a symmetrization E ( * ) of a quasi-Banach function space E is an important construction covering several classical classes of Banach function spaces (see [12,13,21,22,[24][25][26] We study Kadec-Klee properties with respect to global (local) convergence in measure.…”

Section: Introductionmentioning

confidence: 99%