On compact operators on the Riesz-difference sequence spaces-II (original) (raw)
On the Riesz difference sequence space
Rendiconti del Circolo Matematico di Palermo, 2008
In this paper, we give the characterization of some classes of compact operators given by matrices on the normed sequence space , which is a special case of the paranormed Riesz-difference sequence space ,. For this purpose, we apply the Hausdorff measure of noncompactness and use some results.
On compact operators on the Riesz Bm-difference sequence space
Iranian Journal of Science and Technology (Sciences), 2011
In this paper, we give the characterization of some classes of compact operators given by matrices on the normed sequence space , which is a special case of the paranormed Riesz-difference sequence space ,. For this purpose, we apply the Hausdorff measure of noncompactness and use some results.
On compact operators and some Euler -difference sequence spaces
Journal of Mathematical Analysis and Applications, 2011
and γ -duals Matrix transformations Compact operators Hausdorff measure of noncompactness Altay and Ba ¸sar (2005) [1] and Altay, Ba ¸sar and Mursaleen (2006) [2] introduced the Euler sequence spaces e t 0 , e t c and e t ∞ . Başarır and Kayıkçı (2009) [3] defined the B (m) -difference matrix and studied some topological and geometric properties of some generalized Riesz B (m) -difference sequence space. In this paper, we introduce the Euler B (m) -difference sequence spaces e t 0 (B (m) ), e t c (B (m) ) and e t ∞ (B (m) ) consisting of all sequences whose B (m)transforms are in the Euler spaces e t 0 , e t c and e t ∞ , respectively. Moreover, we determine the α-, β-and γ -duals of these spaces and construct the Schauder basis of the spaces e t 0 (B (m) ) and e t c (B (m) ). Finally, we characterize some matrix classes concerning the spaces e t 0 (B (m) ) and e t c (B (m) ) and give the characterization of some classes of compact operators on the sequence spaces e t 0 (B (m) ) and e t ∞ (B (m) ).
Compact operators on Riesz difference sequence space of fractional order
FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020)
In this paper we study the domain of generalized Riesz difference matrix R q Δ (α) of fractional order α in the classical sequence spaces c 0 and c and introduced the sequence spaces r 0 q (Δ (α)) and r c q (Δ (α)). We obtain the α−, β− and γ−duals of these spaces and using Hausdorff measure of noncompactness, we characterize certain classes of compact operators on the space r 0 q (Δ (α)).
On the generalized Riesz B-difference sequence spaces
Filomat, 2010
In this paper, we define the new generalized Riesz B-difference sequence spaces r q ∞ (p, B) , r q c (p, B) , r q 0 (p, B) and r q (p, B) which consist of the sequences whose R q 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 α−, β− and γ−duals of these spaces. Also we determine the neccesary and sufficient conditions on the matrix transformations from these spaces into l∞ and c.
On compact operators and some Euler B ( m ) -difference sequence spaces
Journal of Mathematical Analysis and Applications, 2011
Keywords: B (m) -difference sequence spaces Schauder basis α-, β-and γ -duals Matrix transformations Compact operators Hausdorff measure of noncompactness Altay and Ba¸sar (2005) [1] and Altay, Ba¸sar and Mursaleen (2006) [2] introduced the Euler sequence spaces e t 0 , e t c and e t ∞ . Başarır and Kayıkçı (2009) [3] defined the B (m) -difference matrix and studied some topological and geometric properties of some generalized Riesz B (m) -difference sequence space. In this paper, we introduce the Euler B (m) -difference sequence spaces e t 0 (B (m) ), e t c (B (m) ) and e t ∞ (B (m) ) consisting of all sequences whose B (m)transforms are in the Euler spaces e t 0 , e t c and e t ∞ , respectively. Moreover, we determine the α-, β-and γ -duals of these spaces and construct the Schauder basis of the spaces e t 0 (B (m) )
Some Generalized Difference Riesz Sequence Spaces and Related Matrix Transformations
2017
The generalized difference Riesz sequence space r (M, ∆n m , u, p, s) of non absolute type was recently introduced and studied by some authors. This paper is devoted to characterize the classes (r M, ∆n m , u, p, s , l∞), r q M, ∆n m , u, p, s , c and (r M, ∆n m , u, p, s , c0) of infinite matrices and characterize a basic theorem where l∞ , c and c0 denotes respectively the space of bounded sequences, space of all convergent sequences and space of all sequences converging to zero.
On Some Difference Sequence Spaces of Weighted Means and Compact Operators
Annals of Functional Analysis, 2011
In the peresent paper, by using generalized weighted mean and difference matrix of order m, we introduce the sequence spaces X(u, v, ∆ (m)), where X is one of the spaces ∞ , c or c 0. Also, we determine the α-, β-and γ-duals of those spaces and construct their Schauder bases for X ∈ {c, c 0 }. Morever, we give the characterization of the matrix mappings on the spaces X(u, v, ∆ m) for X ∈ { ∞ , c, c 0 }. Finally, we characterize some classes of compact operators on the spaces ∞ (u, v, ∆ m) and c 0 (u, v, ∆ m) by using the Hausdorff measure of noncompactness.
On some Euler B (m) difference sequence spaces and compact operators
Keywords: B (m) -difference sequence spaces Schauder basis α-, β-and γ -duals Matrix transformations Compact operators Hausdorff measure of noncompactness Altay and Ba¸sar (2005) [1] and Altay, Ba¸sar and Mursaleen (2006) [2] introduced the Euler sequence spaces e t 0 , e t c and e t ∞ . Başarır and Kayıkçı (2009) [3] defined the B (m) -difference matrix and studied some topological and geometric properties of some generalized Riesz B (m) -difference sequence space. In this paper, we introduce the Euler B (m) -difference sequence spaces e t 0 (B (m) ), e t c (B (m) ) and e t ∞ (B (m) ) consisting of all sequences whose B (m)transforms are in the Euler spaces e t 0 , e t c and e t ∞ , respectively. Moreover, we determine the α-, β-and γ -duals of these spaces and construct the Schauder basis of the spaces e t 0 (B (m) )