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Some new sequence spaces derived by the domain of generalized difference matrix. (English) Zbl 1201.40001
Summary: Let λ denote any one of the classical spaces ,c,c 0 and p of bounded, convergent, null and absolutely p-summable sequences, respectively, and λ ^ also be the domain of the generalized difference matrix B(r,s) in the sequence space λ, where 1p<. The present paper is devoted to studying on the sequence space λ ^. Furthermore, the β- and γ-duals of the space λ ^ are determined, and the Schauder bases for the spaces c 0 ^, 1 ^ and p ^ are given, and some topological properties of the spaces c 0 ^, 1 ^ and p ^ are examined. Finally, the classes λ 1 :λ 2 ^ and λ ^ 1 :λ ^ 2 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
46A45Sequence spaces
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