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Strictly singular and cosingular operators

  • Eric Martens (a1)

Abstract

The results given here are a natural continuation of those given by G. P. Shannon (4). The extension of various operators to the completions of the respective spaces are considered and the adjoint operator is more closely examined. A perturbation result for strictly cosingular operators is also given.

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References

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(1)Grothendieck, A.Espaces vectoriels topologiques (Sao Paulo, 1958).
(2)Kelley, J. L., Namioka, I. et al. Linear topological spaces (van Nostrand, 1963).
(3)Robertson, W.Completions of topological vector spaces. Proc. London Math. Soc. (3) 8 (1958), 242–57.
(4)Shannon, G. P.Strictly singular and strictly cosingular operators on topological vector spaces. Proc. Roy. Irish Acad. 73A (1973), 303–8.
(5)Van Dulst, D.On strictly singular operators. Compositio Math. 23 (1971), 169–83.

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