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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A rigid space homeomorphic to Hilbert space
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by Nguyen To Nhu and Paul Sisson PDF
Proc. Amer. Math. Soc. 126 (1998), 85-95 Request permission


A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. This is in sharp contrast to the behavior of operators on $\ell _{2}$, and so rigid spaces are, from the viewpoint of functional analysis, fundamentally different from Hilbert space. Nevertheless, we show in this paper that a rigid space can be constructed which is topologically homeomorphic to Hilbert space. We do this by demonstrating that the first complete rigid space can be modified slightly to be an AR-space (absolute retract), and thus by a theorem of Dobrowolski and Torunczyk is homeomorphic to $\ell _{2}$.
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Additional Information
  • Nguyen To Nhu
  • Affiliation: Institute of Mathematics at Hanoi, P.O. Box 631, Bo Ho, Hanoi, Vietnam
  • Address at time of publication: Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003
  • Email:
  • Paul Sisson
  • Affiliation: Department of Mathematics, Louisiana State University - Shreveport, One University Place, Shreveport, Louisiana 71115
  • Email:
  • Received by editor(s): January 23, 1996
  • Communicated by: James West
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 85-95
  • MSC (1991): Primary 46A16, 54F65; Secondary 46C05, 54G15
  • DOI:
  • MathSciNet review: 1459139