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On Property β of Rolewicz in Köthe-Bochner Function Spaces

100%
Kolwicz P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2005
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tom 53
|
nr 1
75-85
EN
It is proved that the Köthe-Bochner function space E(X) has property β if and only if X is uniformly convex and E has property β. In particular, property β does not lift from X to E(X) in contrast to the case of Köthe-Bochner sequence spaces.
2
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Local structure of generalized Orlicz−Lorentz function spaces

100%
Kolwicz P.
Commentationes Mathematicae
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2015
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tom 55
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nr 2
EN
We study the local structure of a separated point \(x\) in the generalized Orlicz-Lorentz space \(\Lambda ^{\varphi }\) which is a symmetrization of the respective Musielak-Orlicz space \(L^{\varphi }\). We present criteria for an \(LM\) point and a \(\mathit{UM}\) point, and sufficient conditions for a point of order continuity and an \(\mathit{LLUM}\) point, in the space \(\Lambda ^{\varphi }\). We prove also a characterization of strict monotonicity of the space \(\Lambda ^{\varphi }\).
3
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On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm

100%
Kolwicz P.
Banach Center Publications
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2005
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tom 68
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nr 1
79-86
EN
We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
4
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Coefficient of orthogonal convexity of some Banach function spaces

64%
Kolwicz P., Rolewicz S.
Studia Mathematica
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2004
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tom 164
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nr 2
121-138
EN
We study orthogonal uniform convexity, a geometric property connected with property (β) of Rolewicz, P-convexity of Kottman, and the fixed point property (see [19, [20]). We consider the coefficient of orthogonal convexity in Köthe spaces and Köthe-Bochner spaces.
5
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On property (β) of Rolewicz in Köthe-Bochner sequence spaces

64%
Hudzik H., Kolwicz P.
Studia Mathematica
|
2004
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tom 162
|
nr 3
195-212
EN
We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend and improve those from [14] and [15].
6
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A note on strict K-monotonicity of some symmetric function spaces

51%
Ciesielski M., Kolwicz P., Płuciennik R.
Commentationes Mathematicae
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2013
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tom 53
|
nr 2
EN
We discuss some sufficient and necessary conditions for strict K-monotonicity of some important concrete symmetric spaces. The criterion for strict monotonicity of the Lorentz space \(\Gamma _{p,w}\) with \(0\)
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