Proceedings of the American Mathematical Society

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



A note on zeroes of real polynomials in $ C(K)$ spaces

Author: Jesús Ferrer
Journal: Proc. Amer. Math. Soc. 137 (2009), 573-577
MSC (2000): Primary 47H60, 46B26
Published electronically: August 19, 2008
MathSciNet review: 2448577
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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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Jesús Ferrer
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjasot (Valencia), Spain

Keywords: Quadratic polynomials, zero-set, $C(K)$ spaces
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.