Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T04:51:03.750Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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