scholarly journals On the Paranormed Nörlund Sequence Space of Nonabsolute Type

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Infinite Matrices ◽  
Geometric Properties ◽  
Alpha Beta

Maddox defined the spaceℓ(p)of the sequencesx=(xk)such that∑k=0∞‍|xk|pk<∞, in Maddox, 1967. In the present paper, the Nörlund sequence spaceNt(p)of nonabsolute type is introduced and proved that the spacesNt(p)andℓ(p)are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the spaceNt(p)are computed and the basis of the spaceNt(p)is constructed. The classes(Nt(p):μ)and(μ:Nt(p))of infinite matrices are characterized. Finally, some geometric properties of the spaceNt(p)are investigated.

scholarly journals Some properties of Generalized Fibonacci difference bounded and $p$-absolutely convergent sequences

2018 ◽  
Vol 36 (1) ◽  
pp. 37 ◽  
Author(s):  
Bipan Hazarika ◽  
Anupam Das
Keyword(s):  
Sequence Space ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Band Matrix ◽  
Inclusion Relations ◽  
Alpha Beta ◽  
Convergent Sequences

The main objective of this paper is to introduced a new sequence space $l_{p}(\hat{F}(r,s)),$ $ 1\leq p \leq \infty$ by using the band matrix $\hat{F}(r,s).$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. We also characterize some matrix classes on the space $l_{p}(\hat{F}(r,s))$ and examine some geometric properties of this space.

scholarly journals On composition operators of Fibonacci matrix and applications of Hausdorff measure of noncompactness

2022 ◽  
Vol 40 ◽  
pp. 1-24
Author(s):  
Bipan Hazarika ◽  
Anupam Das ◽  
Emrah Evren Kara ◽  
Feyzi Basar
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Composition Operators ◽  
Compact Operators ◽  
Hausdorff Measure Of Noncompactness ◽  
Infinite Matrices ◽  
Geometric Properties ◽  
Matrix Classes ◽  
Alpha Beta ◽  
Fibonacci Matrix

The aim of the paper is introduced the composition of the two infinite matrices $\Lambda=(\lambda_{nk})$ and $\widehat{F}=\left( f_{nk} \right).$ Further, we determine the $\alpha$-, $\beta$-, $\gamma$-duals of new spaces and also construct the basis for the space $\ell_{p}^{\lambda}(\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\ell_{\infty}^{\lambda}(\widehat{F})$ and $\ell_{p}^{\lambda}(\widehat{F}).$ We also investigate some geometric properties concerning Banach-Saks type $p.$Finally we characterize the subclasses $\mathcal{K}(X:Y)$ of compact operators by applying the Hausdorff measure of noncompactness, where $X\in\{\ell_{\infty}^{\lambda}(\widehat{F}),\ell_{p}^{\lambda}(\widehat{F})\}$ and $Y\in\{c_{0},c, \ell_{\infty}, \ell_{1}, bv\},$ and $1\leq p<\infty.$

scholarly journals Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spacesℓpandℓ∞

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Feyzi Başar ◽  
Ali Karaisa
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Geometric Properties ◽  
Modulus Of Convexity ◽  
Inclusion Relations ◽  
Alpha Beta

We introduce the sequence spaceℓpλ(B)of none absolute type which is ap-normed space andBKspace in the cases0<p<1and1⩽p⩽∞, respectively, and prove thatℓpλ(B)andℓpare linearly isomorphic for0<p⩽∞. Furthermore, we give some inclusion relations concerning the spaceℓpλ(B)and we construct the basis for the spaceℓpλ(B), where1⩽p<∞. Furthermore, we determine the alpha-, beta- and gamma-duals of the spaceℓpλ(B)for1⩽p⩽∞. Finally, we investigate some geometric properties concerning Banach-Saks typepand give Gurarii's modulus of convexity for the normed spaceℓpλ(B).

scholarly journals Dual pairs of sequence spaces

2001 ◽  
Vol 28 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Johann Boos ◽  
Toivo Leiger
Keyword(s):  
Sequence Space ◽  
Dual Pair ◽  
General Concept ◽  
Sequence Spaces ◽  
Dual Pairs ◽  
The Third ◽  
Convex Sequence ◽  
Starting Point ◽  
Alpha Beta ◽  
Locally Convex

The paper aims to develop for sequence spacesEa general concept for reconciling certain results, for example inclusion theorems, concerning generalizations of the Köthe-Toeplitz dualsE×(×∈{α,β})combined with dualities(E,G),G⊂E×, and theSAK-property (weak sectional convergence). TakingEβ:={(yk)∈ω:=𝕜ℕ|(ykxk)∈cs}=:Ecs, wherecsdenotes the set of all summable sequences, as a starting point, then we get a general substitute ofEcsby replacingcsby any locally convex sequence spaceSwith sums∈S′(in particular, a sum space) as defined by Ruckle (1970). This idea provides a dual pair(E,ES)of sequence spaces and gives rise for a generalization of the solid topology and for the investigation of the continuity of quasi-matrix maps relative to topologies of the duality(E,Eβ). That research is the basis for general versions of three types of inclusion theorems: two of them are originally due to Bennett and Kalton (1973) and generalized by the authors (see Boos and Leiger (1993 and 1997)), and the third was done by Große-Erdmann (1992). Finally, the generalizations, carried out in this paper, are justified by four applications with results around different kinds of Köthe-Toeplitz duals and related section properties.

scholarly journals Domain of the Double Sequential Band Matrix in the Sequence Space

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Havva Nergiz ◽  
Feyzi Başar
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Transformations ◽  
Difference Matrix ◽  
Band Matrix ◽  
Alpha Beta

The sequence space was introduced by Maddox (1967). Quite recently, the domain of the generalized difference matrix in the sequence space has been investigated by Kirişçi and Başar (2010). In the present paper, the sequence space of nonabsolute type has been studied which is the domain of the generalized difference matrix in the sequence space . Furthermore, the alpha-, beta-, and gamma-duals of the space have been determined, and the Schauder basis has been given. The classes of matrix transformations from the space to the spaces ,candc0have been characterized. Additionally, the characterizations of some other matrix transformations from the space to the Euler, Riesz, difference, and so forth sequence spaces have been obtained by means of a given lemma. The last section of the paper has been devoted to conclusion.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

2021 ◽  
Vol 71 (6) ◽  
pp. 1375-1400
Author(s):  
Feyzi Başar ◽  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
The Matrix ◽  
Alpha Beta ◽  
Necessary And Sufficient ◽  
Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

scholarly journals On the Riesz Almost Convergent Sequences Space

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Mehmet Şengönül ◽  
Kuddusi Kayaduman
Keyword(s):  
Sequence Space ◽  
Sufficient Conditions ◽  
Riesz Transforms ◽  
Necessary And Sufficient Conditions ◽  
Infinite Matrices ◽  
Necessary And Sufficient ◽  
Convergent Sequences

The purpose of this paper is to introduce new spaces and that consist of all sequences whose Riesz transforms of order one are in the spaces and , respectively. We also show that and are linearly isomorphic to the spaces and , respectively. The and duals of the spaces and are computed. Furthermore, the classes and of infinite matrices are characterized for any given sequence space and determine the necessary and sufficient conditions on a matrix to satisfy , for all .

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.

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