J Austral Math Soc Ser A 48 pp214--222, 1990.

Linear Operators in l₂ with a Universality Property

Michael Edelstein and Raymond D. Holmes

Abstract

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 Î F there is P Î P with hf = Ph. While similar results were obtained by Baayen and De Groot, our construction makes is 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.

1980 AMS Subject Classification (1985 Revision): 46C05, 54C05

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Authors

Michael Edelstein

Raymond D. Holmes

Dalhousie University, Halifax, Nova Scotia, Canada.