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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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 note on zeroes of real polynomials in $C(K)$ spaces
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by Jesús Ferrer PDF
Proc. Amer. Math. Soc. 137 (2009), 573-577 Request permission

Abstract:

For real $C(K)$ spaces, we show that being injected in a Hilbert space is a 3-space property. As a consequence, we obtain that, when $K$ does not carry a strictly positive Radon measure, every quadratic continuous homogeneous real-valued polynomial on $C(K)$ admits a linear zero subspace enjoying a property which implies non-separability.
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Additional Information
  • Jesús Ferrer
  • Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjasot (Valencia), Spain
  • Email: Jesus.Ferrer@uv.es
  • Received by editor(s): January 23, 2008
  • Published electronically: August 19, 2008
  • Additional Notes: The author has been partially supported by MEC and FEDER Project MTM2005-08210
  • Communicated by: Nigel J. Kalton
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 573-577
  • MSC (2000): Primary 47H60, 46B26
  • DOI: https://doi.org/10.1090/S0002-9939-08-09574-9
  • MathSciNet review: 2448577