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Zbl 1096.46005
Aydin, Cafer; Başar, Feyzi
Some new sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$.
(English)
[J] Demonstr. Math. 38, No. 3, 641-656 (2005). ISSN 0420-1213

Summary: We introduce the sequence space $a_p^r$ of non-absolute type and prove that the spaces $a_p^r$ and $\ell_p$ are linearly isomorphic for $0<p\le\infty$. We also show that $a_p^r$, which includes the space $\ell_p$, is a $p$-normed space and a BK space in the cases of $0<p<1$ and $1\le p\le\infty$, respectively. Furthermore, we give some inclusion relations and determine the $\alpha$-, $\beta$- and $\gamma$-duals of the space $a_p^r$ and construct its basis. We devote the last section of the paper to the characterization of the matrix mappings from the space $a_p^r$ to some of the known sequence spaces and to some new sequence spaces.
MSC 2000:
*46A45 Sequence spaces
46B45 Banach sequence spaces
46A35 Summability and bases in topological linear spaces

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