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Some new sequence spaces derived by the domain of the triple band matrix. (English) Zbl 1228.40006
Summary: Let λ denote any of the classical spaces ,c,c 0 , and 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 p (B) are given, and some topological properties of the spaces c 0 (B), 1 (B), and 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 ,c,c 0 , p , 1 and λ 2 ,c,c 0 , 1 .
MSC:
40C05Matrix methods in summability
40H05Functional analytic methods in summability
46B45Banach sequence spaces
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