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Some new paranormed sequence spaces. (English) Zbl 1049.46002
Summary: I. J. Maddox defined the sequence spaces (p),c(p) and c 0 (p) in [Proc. Camb. Philos. Soc. 64, 335–340 (1968; Zbl 0157.43503), Q. J. Math., Oxf. (2) 18, 345–355 (1967; Zbl 0156.06602)]. In the present paper, the sequence spaces a 0 r (u,p) and a c r (u,p) of non-absolute type are introduced and it is proved that the spaces a 0 r (u,p) and a c r (u,p) are linearly isomorphic to the spaces c 0 (p) and c(p), respectively. Besides this, the α-, β- and γ-duals of the spaces a 0 r (u,p) and a c r (u,p) are computed and their bases are constructed. Finally, a basic theorem is given and some matrix mappings from a 0 r (u,p) to the sequence spaces of Maddox and to new sequence spaces are characterized.
46A45Sequence spaces