Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞. (14th November 2013)

• Record Type: Journal Article
• Authors: Başar, Feyzi; Karaisa, Ali
• Other Names: Chu Y.-M. Academic Editor.; Stamova I. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-11-14
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/349346
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : We introduce the sequence space ℓ p λ ( B ) of none absolute type which is a p -normed space and B K space in the cases 0 < p < 1 and 1 ⩽ p ⩽ ∞, respectively, and prove that ℓ p λ ( B ) and ℓ p are linearly isomorphic for 0 < p ⩽ ∞ . Furthermore, we give some inclusion relations concerning the space ℓ p λ ( B ) and we construct the basis for the space ℓ p λ ( B ), where 1 ⩽ p < ∞ . Furthermore, we determine the alpha-, beta- and gamma-duals of the space ℓ p λ ( B ) for 1 ⩽ p ⩽ ∞ . Finally, we investigate some geometric properties concerning Banach-Saks type p and give Gurarii's modulus of convexity for the normed space ℓ p λ ( B ) .