Riv.Mat.Univ.Parma (5) 1 (1992)


On (λ, σμ)-bases

Pages: 1-10
Received: 18 September 1991   
Mathematics Subject Classification: 46A45

Abstract This article is devoted to the study of λ-bases, wherein λ is equipped with the more general topology, called σμ-topology, introduced by Ruckle, μ being an arbitrary sequence space. We characterize analytically fully-λ-bases and fullu-λμ-bases. Efforts have been made to identify topologically a sequentially complete space, having a fully-λ-base (or a fully-λμ-base), with a Köthe space, thereby providing a far reaching generalization of the famous classical theorem, which tells that a sequentially complete space with an absolute base is nothing but a Köthe space. Most of the results are motivated by their corresponding analogues in the case of traditional normal topology.