On some topological properties of generalized difference sequence spaces. (1st December 2000)

• Record Type: Journal Article
• Authors: Et, Mikail
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 24:Number 11(2000)
• Page Start: 785
• Page End: 791
• Publication Date: 2000-12-01
• Subjects: Difference sequence spaces -- statistical convergence -- the N-dual -- the pα- -- pβ- -- and pγ-dual; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171200002325
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : We obtain some topological results of the sequence spacesΔ m ( X ), whereΔ m ( X ) = { x = ( x k ) : ( Δ m x k ) ∈ X }, ( m ∈ ℕ ), andX is any sequence space. We compute thep α -, p β -, andp γ -duals ofl ∞, c, andc 0 and we investigate theN -(or null) dual of the sequence spacesΔ m ( l ∞ ), Δ m ( c ), andΔ m ( c 0 ) . Also we show that any matrix map fromΔ m ( l ∞ ) into aB K -space which does not contain any subspace isomorphic toΔ m ( l ∞ ) is compact.