Some new sequence spaces derived by the domain of the triple band matrix

Abstract

Let λ denote any of the classical spaces ℓ ∞ , c , c 0 , and ℓ p of bounded, convergent, null, and absolutely p -summable sequences, respectively, and let λ ( B ) also be the domain of the triple band matrix B ( r , s , t ) in the sequence space λ , where 1 < p < ∞ . The present paper is devoted to studying the sequence space λ ( B ) . Furthermore, the β - and γ -duals of the space λ ( B ) are determined, the Schauder bases for the spaces c ( B ) , c 0 ( B ) , and ℓ p ( B ) are given, and some topological properties of the spaces c 0 ( B ) , ℓ 1 ( B ) , and ℓ p ( B ) are examined. Finally, the classes ( λ 1 ( B ) : λ 2 ) and ( λ 1 ( B ) : λ 2 ( B ) ) of infinite matrices are characterized, where λ 1 ∈ { ℓ ∞ , c , c 0 , ℓ p , ℓ 1 } and λ 2 ∈ { ℓ ∞ , c , c 0 , ℓ 1 } .