A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix $widehat{widehat{B}}$
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Tarih
2022
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
This study serves for analysing algebraic and topological characteristics of the sequence spaces $X(widehat{widehat{B}}(r,s))$ constituted by using non-zero real number $r$ and $s$, where $X$ denotes arbitrary of the classical sequence spaces $ell_{infty}, c, c_{0} $ and $ell_{p}$ $(1<p<infty)$ of bounded, convergent, null and absolutely $p$-summable sequences, respectively and $X(widehat{widehat{B}})$ also is the domain of the matrix $widehat{widehat{B}}(r,s)$ in the sequence space $X$. Briefly, the $beta$- and $gamma$-duals of the space $X(widehat{widehat{B}})$ are computed, and Schauder bases for the spaces $c(widehat{widehat{B}})$, $c_{0}(widehat{widehat{B}})$ and $ell_{p}(widehat{widehat{B}})$ are determined, and some algebraic and topological properties of the spaces $c_{0}(widehat{widehat{B}})$, $ell_{1}(widehat{widehat{B}})$ and $ell_{p}(widehat{widehat{B}})$ are studied. Additionally, it is observed that all these spaces have some remarkable features, including the classes $(X_{1}(widehat{widehat{B}})$: $X_{2})$ and $(X_{1}(widehat{widehat{B}}): X_{2}(widehat{widehat{B}}))$ of infinite matrices which are characterized, in which $X_{1}in{ ell_{infty},c,c_{0},ell_{p},ell_{1}}$ and $X_{2}in{ell_{infty},c,c_{0},ell_{1}}$.
Açıklama
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Kaynak
Fundamental journal of mathematics and applications (Online)
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Cilt
5
Sayı
1
