The Journal of the Indian Mathematical Society

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Kothe-Toeplitz and Topological Duals of Spaces of Strongly Summable Vector Sequences


Affiliations
1 Department of Mathematics & Statistics, D.D.U. Gorakhpur University, Gorakhpur-273009, India
     

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We characterize generalized α-, β- and γ-duals of the spaces of strongly summable vector sequences l{X,p),C0(X,p), c(X,p) and l∞(X, p) where sequences are taken from a Hausdorff locally convex space X. Besides the investigations of some topological properties we determine topological duals of l(X, p), c0(X, p) and c(X, p) when considered with the natural linear topologies on them generated by the family of paranorms.
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  • Kothe-Toeplitz and Topological Duals of Spaces of Strongly Summable Vector Sequences

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Authors

J. K. Srivastava
Department of Mathematics & Statistics, D.D.U. Gorakhpur University, Gorakhpur-273009, India

Abstract


We characterize generalized α-, β- and γ-duals of the spaces of strongly summable vector sequences l{X,p),C0(X,p), c(X,p) and l∞(X, p) where sequences are taken from a Hausdorff locally convex space X. Besides the investigations of some topological properties we determine topological duals of l(X, p), c0(X, p) and c(X, p) when considered with the natural linear topologies on them generated by the family of paranorms.