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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.
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Abstract

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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

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3. Nadler, S. B. Jr, A note on an iterative test of Edelstein, Canad. Math. Bull., (to appear).Google Scholar