The binomial sequence spaces of nonabsolute type
Abstract In this paper, we introduce the binomial sequence spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ of nonabsolute type which include the spaces c 0 $c_{0}$ and c, respectively. Also, we prove that the spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ are linearly isomorph...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-11-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1256-0 |
| Summary: | Abstract In this paper, we introduce the binomial sequence spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ of nonabsolute type which include the spaces c 0 $c_{0}$ and c, respectively. Also, we prove that the spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ are linearly isomorphic to the spaces c 0 $c_{0}$ and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their α-, β-, and γ-duals. Finally, we characterize some matrix classes related to those spaces. |
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| ISSN: | 1029-242X |