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Linear operators in l2 with a universality property
Part of:
Maps and general types of spaces defined by maps
Normed linear spaces and Banach spaces; Banach lattices
Published online by Cambridge University Press: 09 April 2009
Abstract
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A collection P of bounded linear operators in l2 is constructed in such a manner that given any separable metric space X, and any countable collection F of continuous self-maps of X, there is a homeomorphism h of X onto a subset of l2 such that for each f ∈ F there is P ∈ P with hf = Ph.
While similar results were obtained by Baayen and Dc Groot, our construction makes it possible to impose additional conditions on h (depending on F). For example, if all the members of F are uniformly continuous then h too can be made uniformly continuous.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1990
References
[1]Baayen, P. C. and DeGroot, J., ‘Linearization of locally compact transformation groups in Hubert space,’ Math. Systems Theory 2 (1968), 363–379.CrossRefGoogle Scholar
[2]DeGroot, J. and McDowell, R. H., ‘Extension of mappings on metric spaces,’ Fund. Math. 48 (1960), 251–263.CrossRefGoogle Scholar
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