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Solution to a problem of Nirenberg concerning expanding maps


Authors: Dean Ives and David Preiss
Journal: Proc. Amer. Math. Soc. 149 (2021), 301-310
MSC (2010): Primary 47H09
DOI: https://doi.org/10.1090/proc/15214
Published electronically: October 20, 2020
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Abstract: By constructing a map of a separable Hilbert space into itself that is continuous, expanding, nonsurjective, and equal to the identity on the unit ball we answer a problem stated by Louis Nirenberg.


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Additional Information

Dean Ives
Affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
Email: dean@math.ucl.ac.uk

David Preiss
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: d.preiss@warwick.ac.uk

DOI: https://doi.org/10.1090/proc/15214
Received by editor(s): March 1, 2020
Received by editor(s) in revised form: May 28, 2020, and May 29, 2020
Published electronically: October 20, 2020
Communicated by: Stephen J. Dilworth
Article copyright: © Copyright 2020 American Mathematical Society