scholarly journals Contractive projections in Orlicz sequence spaces

2004 ◽  
Vol 2004 (2) ◽  
pp. 133-145 ◽  
Author(s):  
Beata Randrianantoanina
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Case ◽  
Square Function ◽  
Second Derivative ◽  
Orlicz Norm ◽  
The Real ◽  
Complemented Subspaces ◽  
Orlicz Sequence Spaces ◽  
Contractive Projections

We characterize norm-one complemented subspaces of Orlicz sequence spacesℓMequipped with either Luxemburg or Orlicz norm, provided that the Orlicz functionMis sufficiently smooth and sufficiently different from the square function. We measure smoothness ofMusingAC1andAC2classes introduced by Maleev and Troyanski in 1991, and the condition forMto be different from a square function is essentially a requirement that the second derivativeM″ofMcannot have a finite nonzero limit at zero. This paper treats the real case; the complex case follows from previously known results.

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).

Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals

2014 ◽  
Vol 64 (6) ◽  
Author(s):  
Manjul Gupta ◽  
Antara Bhar
Keyword(s):  
Banach Space ◽  
Structural Properties ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Spaces ◽  
Vector Valued

AbstractIn this paper we introduce generalized or vector-valued Orlicz-Lorentz sequence spaces l p,q,M(X) on Banach space X with the help of an Orlicz function M and for different positive indices p and q. We study their structural properties and investigate cross and topological duals of these spaces. Moreover these spaces are generalizations of vector-valued Orlicz sequence spaces l M(X) for p = q and also Lorentz sequence spaces for M(x) = x q for q ≥ 1. Lastly we prove that the operator ideals defined with the help of scalar valued sequence spaces l p,q,M and additive s-numbers are quasi-Banach operator ideals for p < q and Banach operator ideals for p ≥ q. The results of this paper are more general than the work of earlier mathematicians, say A. Pietsch, M. Kato, L. R. Acharya, etc.

scholarly journals One-complemented subspaces of Musielak–Orlicz sequence spaces

2004 ◽  
Vol 130 (1) ◽  
pp. 1-37 ◽  
Author(s):  
J.E. Jamison ◽  
A. Kamińska ◽  
G. Lewicki
Keyword(s):  
Sequence Spaces ◽  
Complemented Subspaces ◽  
Orlicz Sequence Spaces
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