scholarly journals Multipliers on Generalized Mixed Norm Sequence Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Oscar Blasco ◽  
Carme Zaragoza-Berzosa
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Norm Space ◽  
Necessary And Sufficient

Given1≤p,q≤∞and sequences of integers(nk)kand(nk′)ksuch thatnk≤nk′≤nk+1, the generalized mixed norm spaceℓℐ(p,q)is defined as those sequences(aj)jsuch that((∑j∈Ik‍|aj|p)1/p)k∈ℓqwhereIk={j∈ℕ0 s.t. nk≤j<nk′},k∈ℕ0. The necessary and sufficient conditions for a sequenceλ=(λj)jto belong to the space of multipliers(ℓℐ(r,s),ℓ𝒥(u,v)), for different sequencesℐand𝒥of intervals inℕ0, are determined.

scholarly journals A note on Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations

1995 ◽  
Vol 18 (4) ◽  
pp. 681-688 ◽  
Author(s):  
B. Choudhary ◽  
S. K. Mishra
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Necessary And Sufficient

In this paper we define the sequence spacesSℓ∞(p),Sc(p)andSc0(p)and determine the Köthe-Toeplitz duals ofSℓ∞(p). We also obtain necessary and sufficient conditions for a matrixAto mapSℓ∞(p)toℓ∞and investigate some related problems.

scholarly journals Mixed-Norm Amalgam Spaces and Their Predual

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 74
Author(s):  
Houkun Zhang ◽  
Jiang Zhou
Keyword(s):  
Duality Theory ◽  
Fractional Integral ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Mixed Norm ◽  
Fractional Integral Operators ◽  
Primal Space ◽  
Necessary And Sufficient ◽  
Amalgam Spaces

In this paper, we introduce mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) and prove the boundedness of maximal function. Then, the dilation argument obtains the necessary and sufficient conditions of fractional integral operators’ boundedness. Furthermore, the strong estimates of linear commutators [b,Iγ] generated by b∈BMO(Rn) and Iγ on mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) are established as well. In order to obtain the necessary conditions of fractional integral commutators’ boundedness, we introduce mixed-norm Wiener amalgam spaces (Lp→,Ls→)(Rn). We obtain the necessary and sufficient conditions of fractional integral commutators’ boundedness by the duality theory. The necessary conditions of fractional integral commutators’ boundedness are a new result even for the classical amalgam spaces. By the equivalent norm and the operators Str(p)(f)(x), we study the duality theory of mixed-norm amalgam spaces, which makes our proof easier. In particular, note that predual of the primal space is not obtained and the predual of the equivalent space does not mean the predual of the primal space.

scholarly journals On the generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

scholarly journals On Certain Sequence Spaces

1981 ◽  
Vol 24 (2) ◽  
pp. 169-176 ◽  
Author(s):  
H. Kizmaz
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Necessary And Sufficient

AbstractIn this paper define the spaces l∞(Δ), c(Δ), and c0(Δ), where for instance l∞(Δ) = {x=(xk):supk |xk -xk + l|< ∞}, and compute their duals (continuous dual, α-dual, β-dual and γ-dual). We also determine necessary and sufficient conditions for a matrix A to map l∞(Δ) or c(Δ) into l∞ or c, and investigate related questions.

Masked factorable matrices

2002 ◽  
Vol 132 (1) ◽  
pp. 245-254
Author(s):  
Gord Sinnamon
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Necessary And Sufficient ◽  
Factorable Matrices

The class of masked factorable matrices is introduced and simple necessary and sufficient conditions are given for matrices in the class to represent bounded transformations between Lebesgue sequence spaces.

scholarly journals FRÉCHET FRAMES, GENERAL DEFINITION AND EXPANSIONS

2014 ◽  
Vol 12 (02) ◽  
pp. 195-208 ◽  
Author(s):  
STEVAN PILIPOVIĆ ◽  
DIANA T. STOEVA
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
General Definition ◽  
Fréchet Space ◽  
Frechet Space ◽  
Bk Space ◽  
Frame Expansions ◽  
Necessary And Sufficient

We define an (X1, Θ, X2)-frame with Banach spaces X2 ⊆ X1, ‖ ⋅ ‖1 ≤ ‖ ⋅ ‖2, and a BK-space [Formula: see text]. Then by the use of decreasing sequences of Banach spaces [Formula: see text] and of sequence spaces [Formula: see text], we define a General Fréchet frame on the Fréchet space [Formula: see text]. We obtain frame expansions of elements of XF and its dual [Formula: see text], as well of some of the generating spaces of XF with convergence in appropriate norms. Moreover, we determine necessary and sufficient conditions for a General pre-Fréchet frame to be a General Fréchet frame, as well as for the complementedness of the range of the analysis operator U : XF → ΘF. Several examples illustrate our investigations.

scholarly journals New matrix domain derived by the matrix product

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1233-1241
Author(s):  
Vatan Karakaya ◽  
Necip Imşek ◽  
Kadri Doğan
Keyword(s):  
Topological Structure ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformation ◽  
Matrix Product ◽  
Difference Matrix ◽  
Matrix Domain ◽  
The Matrix ◽  
Necessary And Sufficient

In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the ?-, ?- and ?- duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c,??.

scholarly journals The application domain of difference type matrix D(r,0,s,0,t) on some sequence spaces

2020 ◽  
pp. 32-32
Author(s):  
Avinoy Paul ◽  
Binod Tripathy
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Application Domain ◽  
Topological Properties ◽  
Difference Type ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Matrix Mappings

In this paper we introduce new sequence spaces with the help of domain of matrix D(r,0,s,0,t), and study some of their topological properties. Further, we determine ? and ? duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of the matrix mappings.

scholarly journals Measures of noncompactness in (N¯qΔ)summable difference sequence spaces

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5459-5470
Author(s):  
Ishfaq Malik ◽  
Tanweer Jalal
Keyword(s):  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Hausdorff Measure Of Noncompactness ◽  
Measures Of Noncompactness ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper we first introduce N?q?summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices A to map these sequence spaces into the spaces c,c0, and l?. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

scholarly journals Compact operators on some generalized mixed norm spaces

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1019-1026
Author(s):  
A. Alotaibi ◽  
E. Malkowsky ◽  
H. Nergiz
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Mixed Norm ◽  
Hausdorff Measure Of Noncompactness ◽  
Mixed Norm Spaces ◽  
Necessary And Sufficient

We establish identities or estimates for the Hausdorff measure of noncompactness of operators from some generalized mixed norm spaces into any of the spaces c0, c, ?1, and [?1, ??]<m(?)>. Furthermore we give necessary and sufficient conditions for the operators in these cases to be compact. Our results are complementary to those in [1, 3, 13].

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