A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix ˆˆBB^^\widehat{\widehat{B}}

Murat CANDAN

doi:https://doi.org/10.33401/fujma.1003752

Article Details

A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix ˆˆBB^^\widehat{\widehat{B}}

Authors:

Murat CANDAN

Publisher:

Fuat USTA

Main Topics:

Mathematics

Journal:

Fundamental Journal of Mathematics and Applications 2022 Vol.5 Issue 1, pp.51-62

Document Type:

Article

Publication Date:

2/2022

Document Language:

English

Document ID (Org No.):

2000422038

pISSN:

2645-8845

DOI:

https://doi.org/10.33401/fujma.1003752

Abstract:

 

This study serves for analysing algebraic and topological characteristics of the sequence spaces X(ˆˆB(r,s))X(B^^(r,s))X(\widehat{\widehat{B}}(r,s)) constituted by using non-zero real number rrr and sss, where XXX denotes arbitrary of the classical sequence spaces ℓ∞,c,c0ℓ∞,c,c0\ell_{\infty}, c, c_{0}  and ℓpℓp\ell_{p} (1<p<∞)(1<p<∞)(1<p<\infty) of bounded, convergent, null and absolutely ppp-summable sequences, respectively and X(ˆˆB)X(B^^)X(\widehat{\widehat{B}}) also is the domain of the matrix ˆˆB(r,s)B^^(r,s)\widehat{\widehat{B}}(r,s) in the sequence space XXX. Briefly, the ββ\beta- and γγ\gamma-duals of the space X(ˆˆB)X(B^^)X(\widehat{\widehat{B}}) are computed, and Schauder bases for the spaces c(ˆˆB)c(B^^)c(\widehat{\widehat{B}}), c0(ˆˆB)c0(B^^)c_{0}(\widehat{\widehat{B}}) and ℓp(ˆˆB)ℓp(B^^)\ell_{p}(\widehat{\widehat{B}}) are determined, and some algebraic and topological properties of the spaces c0(ˆˆB)c0(B^^)c_{0}(\widehat{\widehat{B}}), ℓ1(ˆˆB)ℓ1(B^^)\ell_{1}(\widehat{\widehat{B}}) and ℓp(ˆˆB)ℓp(B^^)\ell_{p}(\widehat{\widehat{B}}) are studied. Additionally, it is observed that all these spaces have some remarkable features, including the classes (X1(ˆˆB)(X1(B^^)(X_{1}(\widehat{\widehat{B}}): X2)X2)X_{2}) and (X1(ˆˆB):X2(ˆˆB))(X1(B^^):X2(B^^))(X_{1}(\widehat{\widehat{B}}) : X_{2}(\widehat{\widehat{B}})) of infinite matrices which are characterized, in which X1∈{ℓ∞,c,c0,ℓp,ℓ1}X1∈{ℓ∞,c,c0,ℓp,ℓ1}X_{1}\in\{ \ell_{\infty},c,c_{0},\ell_{p},\ell_{1}\} and X2∈{ℓ∞,c,c0,ℓ1}X2∈{ℓ∞,c,c0,ℓ1}X_{2}\in\{\ell_{\infty},c,c_{0},\ell_{1}\}.

Article Details

A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix ˆˆBB^^\widehat{\widehat{B}}

Authors: Murat CANDAN

Publisher: Fuat USTA

Main Topics: Mathematics

Journal: Fundamental Journal of Mathematics and Applications 2022 Vol.5 Issue 1, pp.51-62

Document Type: Article

Publication Date: 2/2022

Document Language: English

Document ID (Org No.): 2000422038

pISSN: 2645-8845

DOI: https://doi.org/10.33401/fujma.1003752

Issues

Authors:

Murat CANDAN

Publisher:

Fuat USTA

Main Topics:

Mathematics

Journal:

Fundamental Journal of Mathematics and Applications 2022 Vol.5 Issue 1, pp.51-62

Document Type:

Article

Publication Date:

2/2022

Document Language:

English

Document ID (Org No.):

2000422038

pISSN:

2645-8845

DOI:

https://doi.org/10.33401/fujma.1003752