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Continuous and Köthe–Toeplitz duals of certain sequence spaces

Published online by Cambridge University Press:  24 October 2008

I. J. Maddox
I. J. Maddox
Affiliation:
University of Lancaster
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Extract

If (X, g) is a paranormed space, with paranorm g (see (2)), then we denote by X* the continuous dual of X, i.e. the set of all continuous linear functionals on X. If E is a set of complex sequences x = (xk) then E† will denote the generalized Köthe–Toeplitz dual of E

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 431 - 435
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Maddox, I. J.Spaces of strongly summable sequences. Quarterly J. Math. Oxford Ser. 2, 18 (1967), 345–55.CrossRefGoogle Scholar
(2)Maddox, I. J.Paranormed sequence spaces generated by infinite matrices. Proc. Cambridge Philos. Soc. 63 (1968).Google Scholar
(3)Simons, S.The sequence spaces l(p ν) and m(p ν). Proc. London Math. Soc. (3), 15 (1965), 422–36.Google Scholar