scholarly journals On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 33-51 ◽  
Author(s):  
M. Mursaleen ◽  
Abdullah Noman
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Bk Space

In the present paper, we introduce the sequence space l?p of non-absolute type and prove that the spaces ??p and lp are linearly isomorphic for 0 < p ? ?. Further, we show that ??p is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ? p ? ?, respectively. Furthermore, we derive some inclusion relations concerning the space ??p. Finally, we construct the basis for the space ??p, where 1 ? p < ?.

scholarly journals On Domain of Nörlund Sequences

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 268 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Fevzi Yaşar
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Sequence Space ◽  
Convergent Series ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Nörlund Matrix ◽  
Inclusion Relations ◽  
The Matrix ◽  
New Space

In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α­, β­, γ­duals, and characterized their matrix transformations on this space and into this space.

scholarly journals On the Dvoretzky-Rogers theorem

1984 ◽  
Vol 27 (2) ◽  
pp. 105-113
Author(s):  
Fuensanta Andreu
Keyword(s):  
Sequence Space ◽  
Normed Space ◽  
Sequence Spaces ◽  
Finite Dimensional ◽  
Banach Sequence Spaces ◽  
Perfect Sequence ◽  
Normal Topology ◽  
Banach Sequence

The classical Dvoretzky-Rogers theorem states that if E is a normed space for which l1(E)=l1{E} (or equivalently , then E is finite dimensional (see [12] p. 67). This property still holds for any lp (l<p<∞) in place of l1 (see [7]p. 104 and [2] Corollary 5.5). Recently it has been shown that this result remains true when one replaces l1 by any non nuclear perfect sequence space having the normal topology (see [14]). In this context, De Grande-De Kimpe [4] gives an extension of the Devoretzky-Rogers theorem for perfect Banach sequence spaces.

scholarly journals New Difference Sequence Spaces Defined by Musielak-Orlicz Function

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Mursaleen ◽  
Sunil K. Sharma ◽  
S. A. Mohiuddine ◽  
A. Kılıçman
Keyword(s):  
Normed Space ◽  
Difference Operator ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Difference Sequence Spaces

We introduce new sequence spaces by using Musielak-Orlicz function and a generalizedB∧ μ-difference operator onn-normed space. Some topological properties and inclusion relations are also examined.

scholarly journals Sequence spaces defined via Euler method and matrix transformations

2021 ◽  
Author(s):  
Pranav Sharma
Keyword(s):  
Normed Space ◽  
Lacunary Sequence ◽  
Euler Method ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Matrix Summability ◽  
Inclusion Relations ◽  
Transformation Methods

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

scholarly journals Almost Sequence Spaces Derived by the Domain of the Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ali Karaisa ◽  
Ümıt Karabıyık
Keyword(s):  
Normed Space ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Matrix Classes ◽  
Almost Convergent Sequence ◽  
Inclusion Relations ◽  
The Matrix

By using , we introduce the sequence spaces , , and of normed space and -space and prove that , and are linearly isomorphic to the sequence spaces , , and , respectively. Further, we give some inclusion relations concerning the spaces , , and the nonexistence of Schauder basis of the spaces and is shown. Finally, we determine the - and -duals of the spaces and . Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.

scholarly journals SOME GENERALIZED FIBONACCI DIFFERENCE SPACES DEFINED BY A SEQUENCE OF MODULUS FUNCTIONS

2017 ◽  
pp. 095 ◽  
Author(s):  
Gülsen Kılınç ◽  
Murat Candan
Keyword(s):  
Real Number ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Inclusion Relations ◽  
Alpha Beta

This paper submits the sequence space $l\left( \widehat{F}\left( r,s\right),\mathcal{F},p,u\right) $ and $l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) $of non-absolute type under the domain ofthe matrix$\widehat{\text{ }F}\left( r,s\right) $ constituted by usingFibonacci sequence and non-zero real number $r$, $s$ and a sequence ofmodulus functions. We study some inclusion relations, topological andgeometric properties of these spaceses. Further, we give the $\alpha $- $%\beta $- and $\gamma $-duals of said sequence spaces and characterization ofthe classes $\left( l\left( \widehat{F}\left( r,s\right) ,\mathcal{F}%,p,u\right) ,X\right) $ and $\left( l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) ,X\right) $.

scholarly journals On Some Properties of New Paranormed Sequence Space of Nonabsolute Type

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
The Other ◽  
Matrix Transformations ◽  
Topological Properties ◽  
Paranormed Sequence Space ◽  
Inclusion Relations

We introduce some new generalized sequence space related to the space . Furthermore we investigate some topological properties as the completeness, the isomorphism, and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute -, -, and -duals of this space and characterize certain matrix transformations on this sequence space.

On some new generalized difference sequence spaces on seminormed spaces defined by a sequence of Orlicz functions

2011 ◽  
Vol 61 (2) ◽  
Author(s):  
Çiğdem Bektaş
Keyword(s):  
Linear Space ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Orlicz Functions ◽  
Inclusion Relations ◽  
Complex Linear ◽  
Difference Sequence Spaces

AbstractIn this paper we define the sequence space ℓ M(Δυm, p, q, s) on a seminormed complex linear space, by using a sequence of Orlicz functions. We study some algebraic and topological properties. We prove some inclusion relations involving ℓ M(Δυm, p, q, s). spaces

scholarly journals Onβ-dual of vector-valued sequence spaces of Maddox

2002 ◽  
Vol 30 (7) ◽  
pp. 383-392 ◽  
Author(s):  
Suthep Suantai ◽  
Winate Sanhan
Keyword(s):  
Sequence Space ◽  
Dual Space ◽  
Sequence Spaces ◽  
Bk Space ◽  
Vector Valued

Theβ-dual of a vector-valued sequence space is defined and studied. We show that if anX-valued sequence spaceEis a BK-space having AK property, then the dual space ofEand itsβ-dual are isometrically isomorphic. We also give characterizations ofβ-dual of vector-valued sequence spaces of Maddoxℓ(X,p),ℓ∞(X,p),c0(X,p), andc(X,p).

scholarly journals Composition of Cesàro and backward difference operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hadi Roopaei ◽  
Bipan Hazarika
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Inclusion Relations

AbstractIn this research, we combine the Cesàro and backward difference operators of different orders which results in introducing a matrix who has two different behaviors and includes several matrices. We also investigate the Köthe duals and inclusion relations of the associated sequence space of this new matrix. Moreover, we compute the norm of this matrix on some well-known sequence spaces.

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