scholarly journals Regular matrix transformation on triple sequence spaces - I

Mathematica ◽  
2018 ◽  
Vol 60 (83) (2) ◽  
pp. 127-139
Author(s):  
Shyamal Debnath ◽  
◽  
Bimal Chandra Das ◽  
2017 ◽  
Vol 35 (1) ◽  
pp. 85 ◽  
Author(s):  
Shyamal Debnath ◽  
Bimal Chandra Das

The main aim of this paper is to introduce the necessary and sufficient condition for a particular type of transformation of the form A: (a......)  be regular from a triple sequence space to another triple sequence space. 


2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar

The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces andc. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator on the sequence spaces andc. Finally, we present a Mercerian theorem. Since the matrix is reduced to a regular matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.


2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Peter Letavaj

AbstractLet F(A) denote the set of all bounded sequences summable by Abel’s method. It is known, that F(A) is a linear subspace of the linear metric space (S, ρ) of all bounded sequences endowed with the sup metric. It is shown in [KOSTYRKO, P.: Convergence fields of regular matrix transformations 2, Tatra Mt. Math. Publ. 40 (2008), 143–147] that the convergence field of a regular matrix transformation is a σ-porous set. We show that F(A) is very porous in S.


Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1233-1241
Author(s):  
Vatan Karakaya ◽  
Necip Imşek ◽  
Kadri Doğan

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,??.


2018 ◽  
Vol 11 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Kuldip Raj ◽  
Anu Choudhary ◽  
Charu Sharma

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over [Formula: see text]-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over [Formula: see text]-normed spaces.


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