Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-18T06:20:00.924Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Contractive Selfmaps of ℓ∞

Published online by Cambridge University Press:  20 November 2018

T. F. McCabe
T. F. McCabe*
Affiliation:
Texas A & M University, College Station, Texas 77843, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note it is shown that a contractive matrix selfmap T of l∞ has T2 a contraction; hence the techniques used in showing ITNC for lp(1 ≤ p < ∞), c0, and c do not apply to l∞.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 421 - 424
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Hardy, G. H., Divergent Series, Oxford, Clarendon Press, 1956.Google Scholar
2. McCave, T. F. and Bryant, Jack, A note on Edelsteir's iterative test and spaces of continuous functions, Pacific J. Math., (to appear).Google Scholar
3. Nadler, S. B. Jr, A note on an iterative test of Edelstein, Canad. Math. Bull., (to appear).Google Scholar