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Nonexpansive Uniformly Asymptotically Stable Flows are Linear

Published online by Cambridge University Press:  20 November 2018

Ludvik Janos ,
Roger C. McCann  and
J. L. Solomon
Ludvik Janos
Affiliation:
Mississippi State UniversityMississippi, 39762
Roger C. McCann
Affiliation:
Mississippi State UniversityMississippi, 39762
J. L. Solomon
Affiliation:
Mississippi State UniversityMississippi, 39762
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Abstract

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We show that if a flow (R, X, π) on a separable metric space (X, d) satisfies (i) the transition mapping π(t, •): X → X is non-expansive for every t ≥ 0; (ii) X contains a globally uniformly asymptotically stable compact invariant subset, then the flow (R, X, π) is linear in the sense that it can be topologically and equivariantly embedded into a flow () on the Hilbert space l2 for which all of the transition mappings are linear operators on l2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 401 - 407
Copyright
Copyright © Canadian Mathematical Society 1981

References

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