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1
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Erratum to the paper "Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm" (Colloq. Math. 65 (1993), 157-164)

100%
Hudzik H., Zbąszyniak Z.
Colloquium Mathematicum
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1993
|
tom 66
|
nr 2
335
2
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On property (β) of Rolewicz in Köthe-Bochner sequence spaces

100%
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].
3
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Smooth points of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm

100%
Hudzik H., Zbąszyniak Z.
Colloquium Mathematicum
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1993
|
tom 65
|
nr 2
157-164
4
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Geometry of quotient spaces and proximinality

81%
Cui Y., Hudzik H., Khongtham Y.
Annales Polonici Mathematici
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2003
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tom 82
|
nr 1
9-18
EN
It is proved that if X is a rotund Banach space and M is a closed and proximinal subspace of X, then the quotient space X/M is also rotund. It is also shown that if Φ does not satisfy the δ₂-condition, then $h⁰_{Φ}$ is not proximinal in $l⁰_{Φ}$ and the quotient space $l⁰_{Φ}/h⁰_{Φ}$ is not rotund (even if $l⁰_{Φ}$ is rotund). Weakly nearly uniform convexity and weakly uniform Kadec-Klee property are introduced and it is proved that a Banach space X is weakly nearly uniformly convex if and only if it is reflexive and it has the weakly uniform Kadec-Klee property. It is noted that the quotient space X/M with X and M as above is weakly nearly uniformly convex whenever X is weakly nearly uniformly convex. Criteria for weakly nearly uniform convexity of Orlicz sequence spaces equipped with the Orlicz norm are given.
5
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Characteristic of monotonicity of Orlicz function spaces equipped with the Orlicz norm

81%
Foralewski P., Hudzik H., Kaczmarek R., Krbec M.
Commentationes Mathematicae
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2013
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tom 53
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nr 2
EN
We first prove that the property of strict monotonicity of a~K\"othe space \((E,\|.\|_E)\) and\slash or of its K\"othe dual \((E',\|.\|_{E'})\) can be used successfully to compare the supports of \(x\in E\backslash\{\theta\}\) and \(y\in S(E')\), where \(=\|x\|_E\). Next we prove that any element \(x\in S_{+}(E)\) with \(\mu(T\backslash\operatorname{supp} x)=0\) is a~point of order smoothness in \(E\), whenever \(E\) is an order continuous K\"othe space. Finally, we present formulas for the characteristic of monotonicity of Orlicz function spaces endowed with the Orlicz norm in the case when the generating Orlicz function does not satisfy suitable \(\Delta_2\)-condition or the measure is non-atomic infinite, and some lower and upper estimates for the characteristic of monotonicity of this spaces when the measure is non-atomic and finite.
6
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Banach-Saks property in some Banach sequence spaces

81%
Cui Y., Hudzik H., Płuciennik R.
Annales Polonici Mathematici
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1996-1997
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tom 65
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nr 2
193-202
EN
It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.
7
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Errata to the paper "Banach-Saks property in some Banach sequence spaces" (Ann. Polon. Math. 65 (1997), 193-202)

81%
Cui Y., Hudzik H., Płuciennik R.
Annales Polonici Mathematici
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1996-1997
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tom 65
|
nr 3
303
8
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Erratum and addendum to the paper "Compactness and essential norms of composition operators on Orlicz-Lorentz spaces" [Applied Mathematics Letters 25 (2012) 1778--1783]

81%
Cui Y., Hudzik H., Kumar R., Kumar R.
Commentationes Mathematicae
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2014
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tom 54
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nr 2
9
Content available remote

A generalized projection decomposition in Orlicz-Bochner spaces

81%
Hudzik H., Płuciennik R., Wang Y.
Banach Center Publications
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2005
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tom 68
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nr 1
61-70
EN
In this paper, a precise projection decomposition in reflexive, smooth and strictly convex Orlicz-Bochner spaces is given by the representation of the duality mapping. As an application, a representation of the metric projection operator on a closed hyperplane is presented.
10
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Uniformly non-$l_{n}^{(1)}$ Orlicz spaces with Luxemburg norm

60%
Hudzik H.
Studia Mathematica
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1985
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tom 81
|
nr 3
271-284
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