scholarly journals Schur property and lP isomorphic copies in Musielak–Orlicz sequence spaces

2007 ◽  
Vol 75 (2) ◽  
pp. 193-210 ◽  
Author(s):  
B. Zlatanov
Keyword(s):  
Sequence Space ◽  
Unit Vector ◽  
Sequence Spaces ◽  
Unit Vector Basis ◽  
Sufficient Condition ◽  
Orlicz Sequence Space ◽  
Property A ◽  
Schur Property ◽  
Vector Basis ◽  
Orlicz Sequence Spaces

The author shows that if the dual of a Musielak–Orlicz sequence space lΦ is a stabilized asymptotic l∞, space with respect to the unit vector basis, then lΦ is saturated with complemented copies of l1 and has the Schur property. A sufficient condition is found for the isomorphic embedding of lp spaces into Musielak–Orlicz sequence spaces.

scholarly journals On some new modular sequence spaces

2013 ◽  
Vol 31 (2) ◽  
pp. 55 ◽  
Author(s):  
Cigdem Asma Bektas ◽  
Gülcan Atıci
Keyword(s):  
Sequence Space ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Orlicz Sequence Space ◽  
Orlicz Functions ◽  
Orlicz Sequence Spaces

Lindenstrauss and Tzafriri [7] used the idea of Orlicz function to define the sequence space ℓM which is called an Orlicz sequence space. Another generalization of Orlicz sequence spaces is due to Woo [9]. An important subspace of ℓ (M), which is an AK-space, is the space h (M) . We define the sequence spaces ℓM (m) and ℓ N(m), where M = (Mk) and N = (Nk) are sequences of Orlicz functions such that Mk and Nk be mutually  complementary for each k. We also examine some topological properties of these spaces. We give the α−, β− and γ− duals of the sequence space h (M) and α− duals of the squence spaces ℓ (M, λ) and ℓ (N, λ).

Banded perturbations of the unit vector basis in some sequence spaces

1978 ◽  
Vol 29 (4) ◽  
pp. 389-392
Author(s):  
Alfred D. Andrew ◽  
Stephen Demko
Keyword(s):  
Unit Vector ◽  
Sequence Spaces ◽  
Unit Vector Basis ◽  
Vector Basis

scholarly journals Linear functionals on Orlicz sequence spaces without local convexity

1992 ◽  
Vol 15 (2) ◽  
pp. 241-254 ◽  
Author(s):  
Marian Nowak
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Local Convexity ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Orlicz Sequence Space ◽  
Orlicz Sequence Spaces ◽  
Locally Convex

The general form of continuous linear functionals on an Orlicz sequence space1ϕ(non-separable and non-locally convex in general) is obtained. It is proved that the spacehϕis anM-ideal in1ϕ.

On the Structure of the Set of Symmetric Sequences in Orlicz Sequence Spaces

2007 ◽  
Vol 50 (1) ◽  
pp. 138-148 ◽  
Author(s):  
Bünyamin Sari
Keyword(s):  
Partial Order ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Orlicz Sequence Space ◽  
Orlicz Sequence Spaces

AbstractWe study the structure of the sets of symmetric sequences and spreading models of an Orlicz sequence space equipped with partial order with respect to domination of bases. In the cases that these sets are “small”, some descriptions of the structure of these posets are obtained.

scholarly journals Packing Constant in Orlicz Sequence Spaces Equipped with the p-Amemiya Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xin He ◽  
Jijie Yu ◽  
Yunan Cui ◽  
Xin Huo
Keyword(s):  
Sequence Space ◽  
Geometric Characteristic ◽  
Orlicz Spaces ◽  
Sequence Spaces ◽  
Orlicz Sequence Space ◽  
Orlicz Sequence Spaces ◽  
Relevant Work ◽  
Amemiya Norm

The problem of packing spheres in Orlicz sequence spacelΦ,pequipped with the p-Amemiya norm is studied, and a geometric characteristic about the reflexivity oflΦ,pis obtained, which contains the relevant work aboutlp  (p>1)and classical Orlicz spaceslΦdiscussed by Rankin, Burlak, and Cleaver. Moreover the packing constant as well as Kottman constant in this kind of spaces is calculated.

Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals

2018 ◽  
Vol 68 (1) ◽  
pp. 115-134 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Space ◽  
Geometric Properties ◽  
Orlicz Functions ◽  
Opial Property ◽  
Uniform Opial Property ◽  
Vector Valued

AbstractIn the present paper we introduce generalized vector-valued Musielak-Orlicz sequence spacel(A,𝓜,u,p,Δr,∥·,… ,·∥)(X) and study some geometric properties like uniformly monotone, uniform Opial property for this space. Further, we discuss the operators ofs-type and operator ideals by using the sequence ofs-number (in the sense of Pietsch) under certain conditions on matrixA.

The structure of l∞ in some generalized Orlicz sequence spaces

2004 ◽  
Vol 41 (4) ◽  
pp. 457-465
Author(s):  
J. Ewert ◽  
Z. Lewandowska
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Porous Set ◽  
Orlicz Sequence Spaces

In this paper we consider the structure of l∞ in the modular sequence space T(A, {fn}) defined in [2]. We obtain the conditions when l∞ = T(A, {fn}). We prove that if l∞ ≠ T(A, {fn}), then the space l∞ is an Fσ, σ-strorigly porous set in T(A, {fn}).

scholarly journals Gliding hump properties and some applications

1995 ◽  
Vol 18 (1) ◽  
pp. 121-132 ◽  
Author(s):  
Johann Boos ◽  
Daniel J. Fleming
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Sufficient Condition ◽  
Sectional Convergence

In this not we consider several types of gliding bump properties for a sequence spaceEand we consider the various implications between these properties. By means of examples we show that most of the implications are strict and they afford a sort of structure between solid sequence spaces and those with weakly sequentially completeβ-duals. Our main result is used to extend a result of Bennett and Kalton which characterizes the class of sequence spacesEwith the properly thatE⊂SF, wheneverFis a separableFKspace containingEwhereSFdenotes the sequences inFhaving sectional convergence. This, in turn, is used to identify a gliding humps property as a sufficient condition forEto be in this class.

scholarly journals Bounded Domains of Generalized Riesz Methods with the Hahn Property

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Maria Zeltser
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Infinite Matrix ◽  
Bounded Domains ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Hausdorff Matrix ◽  
Additional Assumptions

In 2002 Bennett et al. started the investigation to which extent sequence spaces are determined by the sequences of 0s and 1s that they contain. In this relation they defined three types of Hahn properties for sequence spaces: the Hahn property, separable Hahn property, and matrix Hahn property. In general all these three properties are pairwise distinct. If a sequence spaceEis solid and(0,1ℕ∩E)β=Eβ=ℓ1then the two last properties coincide. We will show that even on these additional assumptions the separable Hahn property and the Hahn property still do not coincide. However if we assumeEto be the bounded summability domain of a regular Riesz matrixRpor a regular nonnegative Hausdorff matrixHp, then this assumption alone guarantees thatEhas the Hahn property. For any (infinite) matrixAthe Hahn property of its bounded summability domain is related to the strongly nonatomic property of the densitydAdefined byA. We will find a simple necessary and sufficient condition for the densitydAdefined by the generalized Riesz matrixRp,mto be strongly nonatomic. This condition appears also to be sufficient for the bounded summability domain ofRp,mto have the Hahn property.

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