Kothe spaces and topological algebra with bases

Nuclear Kothe sequence space λ(P) its crossdual λ(P) xand 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∞ and c0 are obtained. In a topological algebra set-up, an abstract Grothendieck-Pietsch nuclearity criterion is developed