Some Topological and Geometrical Properties of a New Difference Sequence Space. (15th February 2011)

• Record Type: Journal Article
• Authors: Demiriz, Serkan; Çakan, Celal
• Other Names: Apreutesei Narcisa C. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2011(2011)
• Publication Date: 2011-02-15
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2011/213878
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We introduce the new difference sequence spacea p r ( Δ ) . Further, it is proved that the spacea p r ( Δ ) is the BK-space including the spaceb v p, which is the space of sequences of pbounded variation. We also show that the spacesa p r ( Δ ), andℓ p are linearly isomorphic for1 ≤ p < ∞ . Furthermore, the basis and theα -, β - andγ - duals of the spacea p r ( Δ ) are determined. We devote the final section of the paper to examine some geometric properties of the spacea p r ( Δ ) .