ON DIFFERENCE ORLICZ SEQUENCE SPACE OF CEZÁRO TYPE

2017 ◽  
Vol 102 (1) ◽  
pp. 97-109
Author(s):  
Ahmad H. A. Bataineh
Keyword(s):  
Sequence Space ◽  
Orlicz Sequence Space

scholarly journals Hermitian operators and isometries on sums of Banach spaces

1989 ◽  
Vol 32 (2) ◽  
pp. 169-191 ◽  
Author(s):  
R. J. Fleming ◽  
J. E. Jamison
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Space ◽  
Reflexive Banach Space ◽  
Geometric Theory ◽  
Orlicz Sequence Space ◽  
Vector Sequence ◽  
Banach Sequence Space ◽  
Banach Sequence

Let E be a Banach sequence space with the property that if (αi) ∈ E and |βi|≦|αi| for all i then (βi) ∈ E and ‖(βi)‖E≦‖(αi)‖E. For example E could be co, lp or some Orlicz sequence space. If (Xn) is a sequence of real or complex Banach spaces, then E can be used to construct a vector sequence space which we will call the E sum of the Xn's and symbolize by ⊕EXn. Specifically, ⊕EXn = {(xn)|(xn)∈Xn and (‖xn‖)∈E}. The E sum is a Banach space with norm defined by: ‖(xn)‖ = ‖(‖xn‖)‖E. This type of space has long been the source of examples and counter-examples in the geometric theory of Banach spaces. For instance, Day [7] used E=lp and Xk=lqk, with appropriate choice of qk, to give an example of a reflexive Banach space not isomorphic to any uniformly conves Banach space. Recently VanDulst and Devalk [33] have considered Orlicz sums of Banach spaces in their studies of Kadec-Klee property.

scholarly journals A counterexample in the theory of Hermitian liftings

1982 ◽  
Vol 25 (2) ◽  
pp. 141-144 ◽  
Author(s):  
D. A. Legg
Keyword(s):  
Sequence Space ◽  
Hermitian Operator ◽  
Compact Perturbation ◽  
Orlicz Sequence Space

In [3], [8], and [2], it was shown that if is an essentially Hermitian operator on l P, 1≦ p<∞, or on Lp[0,1], 1< p<∞, then T is a compact perturbation of a Hermitian operator. In [1], this result was established for operators on Orlicz sequence space l M, where 2∉[α M,β M] (the associated interval for M). In that same paper, it was conjectured that this result does not in general hold if 2∈[α M,β M]. In this paper, we show that this conjecture is correct by exhibiting an Orlicz sequence space l M and an essentially Hermitian operator on l M which is not a compact perturbation of a Hermitian operator.

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).

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.

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 Nonsquare Constants of Orlicz Spaces with Orlicz Norm

2003 ◽  
Vol 55 (1) ◽  
pp. 204-224 ◽  
Author(s):  
Yaqiang Yan
Keyword(s):  
Function Space ◽  
Sequence Space ◽  
Orlicz Spaces ◽  
Orlicz Sequence Space ◽  
Orlicz Norm ◽  
And Function ◽  
Equivalent Expressions

AbstractLet lΦ and LΦ(Ω) be the Orlicz sequence space and function space generated by N-function Φ(u) with Orlicz norm. We give equivalent expressions for the nonsquare constants CJ(lΦ), CJ(LΦ(Ω)) in sense of James and CS(lΦ), CS(LΦ(Ω)) in sense of Schäffer. We are devoted to get practical computational formulas giving estimates of these constants and to obtain their exact value in a class of spaces lΦ and LΦ(Ω).

Sign in / Sign up

Export Citation Format

Share Document