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Köthe spaces and topological algebra with bases

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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∞ andc 0 are obtained. In a topological algebra set-up, an abstract Grothendieck-Pietsch nuclearity criterion is developed.

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Authors and Affiliations

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

    Subhash J. Bhatt & G. M. Deheri

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  1. Subhash J. Bhatt
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  2. G. M. Deheri
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Bhatt, S.J., Deheri, G.M. Köthe spaces and topological algebra with bases. Proc. Indian Acad. Sci. (Math. Sci.) 100, 259–273 (1990). https://doi.org/10.1007/BF02837849

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