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1
Content available remote On symmetric spaces containing isomorphic copies of Orlicz sequence spaces
Astashkin S.
Commentationes Mathematicae
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2016
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Vol 56, No. 1
29--44
EN
Let an Orlicz function N be (1+ε)-convex and (2−ε)-concave at zero for some ε>0. Then the function 1/N−1(t), t∈(0,1], belongs to a separable symmetric space X with the Fatou property, which is an interpolation space with respect to the couple (L1,L2), whenever X contains a strongly embedded subspace isomorphic to the Orlicz sequence space lN. On the other hand, we find necessary and sufficient conditions on such an Orlicz function N under which a sequence of mean zero independent functions equimeasurable with the function 1/N−1(t), 0-1(t), a strongly embedded subspace isomorphic to the Orlicz sequence lN.
2
Content available remote Sequences of bounded φ-variation and weighted unconditional convergence of series
Musielak J.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
153--162
EN
There are investigated spaces v0,φ of sequences of bounded φ-variation. Spaces v0, φ are applied to the problem of weighted unconditional convergence of series. It is shown that (vo,φ,lφ* ), where lφ* means the Orlicz sequence space generated by the N-function φ*, is a pair of weighted unconditional convergence. There are also considered nonlinear convolution - type operators in v0,φ .
3
Content available remote Orlicz-Bochner sequence spaces that have the uniform λ-property
Shi Z., Zhang P.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2004
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Vol. 44, nr spec.
215-227
EN
Necessary and sufficient conditions in order that Orlicz-Bochner sequence spaces equipped with Luxemburg norm have the uniform [lambda] property are given.
4
Content available remote Formulae for nonsquare constants of Orlicz sequence spaces with Orlicz norm
Yan Y.
Bulletin of the Polish Academy of Sciences. Mathematics
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2003
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Vol. 51, no 3
233-246
EN
Let l^phi be the Orlicz Sequence space generated by a N-function Phi(u) equipped with the Orlicz norm, phi be the right derivative of Phi. We show that the nonsquare constants Cj (l^phi] in the sense of James and Cj (l^phi ) in the sense of Schaffer satisfy: (i) if phi is concave, then Cj(l^phi) = sup inf [...], (ii) if phi is convex, then Cs(l^phi) = inf inf [...]. With this result we obtain some formulae for practical computation of non-square constants.
5
Content available remote Property (L) in Orlicz sequence spaces equipped with the Luxemburg norm
ChunXue W., Cui Y.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2003
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[Z] 43(2)
301-309
EN
In this paper, we prove that a banach space X with the property (L) with respect to the function [ro](r,s) has the uniform Opial property if and only if [ro](1,s)>1 for any s>0. The criterion in order that an Orlicz sequence space equipped with the Luxemburg norm has the property (L) is given.
6
Content available remote Generalizations of the c0-l1-l∞ theorem of Bessaga and Pełczyński
Wójtowicz M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2002
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Vol. 50, no 4
373-382
EN
Let X and Y be two Banach spaces such that Y has a subsymmetric Schauder basis (yn). We study the consequences of the following assumption: X* has a subspace isomorphic to Y. If the basis is shrinking, then X* contains a copy of Y** (Proposition 1), and if X has the so-called controlled separable projection property (in particular, if X is weakly compactly determined), then X* contains a copy of [yn*]* (Theorem 1). These results are applied for Orlicz sequence spaces.
7
Content available remote Strongly extreme points in Orlicz sequence spaces
Wisła M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2001
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[Z] 41
241-255
EN
Let l^[fi] be an Orlicz space endowed with the Luxemburg norm. The main result reads as flooows: the set of all strongly extreme points of the unit ball B(l^[fi]) is nonempty iff it coincides with the set of all extreme points of B(l^[fi]) iff the function [fi] either satisfies the condition [ro]_2 or vanishes at some point outside zero.
8
Content available remote On some local and global geometry of Orlicz sequence spaces endowed with the Orlicz norm
Hao C., Li Y., Wang T.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2000
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[Z] 40
69-91
EN
A critetion of URWC point in Orlicz sequence spaces endowed with the Orlicz norm is given. As a corollary, we get a criterion in order that a space has LURWC property.
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