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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/100/03/0259-0273

    • Keywords

       

      Köthe sequence spaces; G1- andG∞-conditions; cross-dual of a sequence space; nuclear locally convex space; Schauder basis; equicontinuous and absolute basis; unconditional convergence; locally convex algebra; orthogonal basis; Grothendieck-Pietsch n

    • Abstract

       

      Nuclear Köthe sequence spaceλ(P) its crossdualλ(P)x and their non-nuclear variants are examined as topological algebras. Modelling on them, a general theory of nuclear topological algebras with orthogonal basis is developed. As a by-product, abstract characterizations of sequence algebras ℓ∞ andc0 are obtained. In a topological algebra set-up, an abstract Grothendieck-Pietsch nuclearity criterion is developed.

    • Author Affiliations

       

      Subhash J Bhatt1 G M Deheri1

      1. Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar - 388 120, India

    • Dates

       
      Published
      December 1990
      Manuscript received
      6 February 1989
      Manuscript revised
      23 March 1990

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