scholarly journals On compact operators on some spaces related to matrix B(r, s)

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 41-51 ◽  
Author(s):  
Ivana Djolovic
Keyword(s):  
Compact Operators ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Subject Classifications ◽  
Mathematics Subject Classifications

Many sequence spaces arise from different concepts of summability. Recent results obtained by Altay, Ba?ar and Malkowsky [2] are related to strong Cesaro summability and boundedness. They determined ?-duals of the new sequence spaces and characterized some classes of matrix transformations on them. Here, we will present new results supplementing their research with the characterization of classes of compact operators on those spaces. 2010 Mathematics Subject Classifications. 46B15, 46B45, 46B50. .

scholarly journals Cesàro Summable Sequence Spaces over the Non-Newtonian Complex Field

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Uğur Kadak
Keyword(s):  
Sequence Spaces ◽  
Matrix Transformations ◽  
Complex Numbers ◽  
Complex Field ◽  
Cesàro Summability ◽  
Summable Sequence ◽  
Cesaro Summability ◽  
Cesàro Method

The spacesω0p,ωp, andω∞pcan be considered the sets of all sequences that are strongly summable to zero, strongly summable, and bounded, by the Cesàro method of order1with indexp. Here we define the sets of sequences which are related to strong Cesàro summability over the non-Newtonian complex field by using two generator functions. Also we determine theβ-duals of the new spaces and characterize matrix transformations on them into the sets of⁎-bounded,⁎-convergent, and⁎-null sequences of non-Newtonian complex numbers.

Some sequence spaces and completeness of normed spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 281-287
Author(s):  
RAMAZAN KAMA ◽  
◽  
BILAL ALTAY ◽  
Keyword(s):  
Normed Space ◽  
Summability Method ◽  
Sequence Spaces ◽  
Normed Spaces ◽  
Cesàro Summability ◽  
Cesaro Summability

In this paper we introduce new sequence spaces obtained by series in normed spaces and Cesaro summability method. We prove that completeness ´ and barrelledness of a normed space can be characterized by means of these sequence spaces. Also we establish some inclusion relationships associated with the aforementioned sequence spaces.

Applications of Statistical Convergence of order (η, δ + γ) in difference sequence spaces of fuzzy numbers

2020 ◽  
pp. 1-9
Author(s):  
Swati Jasrotia ◽  
Uday Pratap Singh ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Cesàro Summability ◽  
Matlab Software ◽  
Cesaro Summability ◽  
Set Up ◽  
Difference Sequence Spaces

In this article, we introduce and study some difference sequence spaces of fuzzy numbers by making use of λ-statistical convergence of order (η, δ + γ) . With the aid of MATLAB software, it appears that the statistical convergence of order (η, δ + γ) is well defined every time when (δ + γ) > η and this convergence fails when (δ + γ) < η. Moreover, we try to set up relations between (Δv, λ)-statistical convergence of order (η, δ + γ) and strongly (Δv, p, λ)-Cesàro summability of order (η, δ + γ) and give some compelling instances to show that the converse of these relations is not valid. In addition to the above results, we also graphically exhibits that if a sequence of fuzzy numbers is bounded and statistically convergent of order (η, δ + γ) in (Δv, λ), then it need not be strongly (Δv, p, λ)-Cesàro summable of order (η, δ + γ).

scholarly journals Completeness of a normed space via strong p-Cesàro summability

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3013-3022 ◽  
Author(s):  
F. Léon-Saavedra ◽  
S. Moreno-Pulido ◽  
A. Sala-Pérez
Keyword(s):  
Normed Space ◽  
Convergent Series ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Weakly Unconditionally Cauchy Series ◽  
Unconditionally Convergent Series ◽  
Cauchy Series

In this paper we will characterize the completeness and barrelledness of a normed space through the strong p-Ces?ro summability of series. A new characterization of weakly unconditionally Cauchy series and unconditionally convergent series through the strong p-Ces?ro summability is obtained.

scholarly journals Approximation numbers of matrix transformations and inclusion maps

2011 ◽  
Vol 42 (2) ◽  
pp. 193-203
Author(s):  
M. Gupta ◽  
L. R. Acharya
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Diagonal Operator ◽  
Approximation Numbers ◽  
Vector Valued

In this paper we establish relationships of the approximation numbers of matrix transformations acting between the vector-valued sequence spaces spaces of the type $\lambda(X)$ defined corresponding to a scalar-valued sequence space $\lambda$ and a Banach space $(X,\|.\|)$ as $$\lambda(X)=\{\overline x=\{x_i\}: x_i\in X, \forall~i\in \mathbb{N},~\{\|x_i\|_X\}\in \lambda\};$$ with those of their component operators. This study leads to a characterization of a diagonal operator to be approximable. Further, we compute the approximation numbers of inclusion maps acting between $\ell^p(X)$ spaces for $1\leq p\leq \infty$.

scholarly journals Ordinary, absolute and strong summability and matrix transformations

Filomat ◽  
2003 ◽  
pp. 59-78 ◽  
Author(s):  
Abdullah Jarrah ◽  
Eberhard Malkowsky
Keyword(s):  
Sufficient Conditions ◽  
Compact Operators ◽  
Strong Summability ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Serbia And Montenegro ◽  
The Past ◽  
Necessary And Sufficient ◽  
The University ◽  
Natural Way

Many important sequence spaces arise in a natural way from various concepts of summability, namely ordinary, absolute and strong summability. In the first two cases they may be considered as the domains of the matrices that define the respective methods of summability; the situation, however, is different and more complicated in the case of strong summability. Given sequence spaces X and Y, we find necessary and sufficient conditions for the entries of a matrix to map X into Y, and characterize the subclass of those matrices that are compact operators. This paper gives a survey of recent research in the field of matrix transformations at the University of Nis Serbia and Montenegro, in the past four years.

scholarly journals On some vector valued multiplier spaces with statistical Cesàro summability

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5135-5147 ◽  
Author(s):  
Ramazan Kama
Keyword(s):  
Sequence Spaces ◽  
Normed Spaces ◽  
Cesàro Summability ◽  
Cesaro Summability ◽  
Vector Valued ◽  
Multiplier Sequence

In the present paper we define and study some vector valued spaces within the frame of the Statistical Ces?ro convergence and the Statistically Ces?ro summability in normed spaces. Also, we characterize the continuous, compact and sequential continuous summing operators on Statistical Ces?ro multiplier sequence spaces.

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