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 $X_{2}\in\{\ell_{\infty},c,c_{0},\ell_{1}\}$.
Matrix domain of a sequence space Schauder basis $\beta-$ and $% \gamma-$duals and matrix transformations
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Erken Görünüm Tarihi | 13 Şubat 2022 |
Yayımlanma Tarihi | 1 Mart 2022 |
Gönderilme Tarihi | 2 Ekim 2021 |
Kabul Tarihi | 11 Şubat 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 5 Sayı: 1 |