Some topological and geometrical properties of a new difference sequence space. (English) Zbl 1228.46005

Demiriz, Serkan; Çakan, Celal

Abstr. Appl. Anal. 2011, Article ID 213878, 14 p. (2011).

Summary: We introduce the new difference sequence space \(a^r_p(\Delta)\). Further, it is proved that the space \(a^r_p(\Delta)\) is a BK-space including the space \(bv_p\), which is the space of sequences of \(p\)-bounded variation. We also show that the spaces \(a^r_p(\Delta)\) and \(\ell_p\) are linearly isomorphic for \(1\leq p<\infty\). Furthermore, the basis and the \(\alpha\)-, \(\beta\)- and \(\gamma\)-duals of the space \(a^r_p(\Delta)\) are determined. We devote the final section of the paper to examine some geometric properties of the space \(a^r_p(\Delta)\).

MSC:

46A45	Sequence spaces (including Köthe sequence spaces)
46B45	Banach sequence spaces

Keywords:

difference sequence space; sequences of \(p\)-bounded variation

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