A note on zeroes of real polynomials in spaces

Author:
Jesús Ferrer

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

Published electronically:
August 19, 2008

MathSciNet review:
2448577

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Abstract | References | Similar Articles | Additional Information

Abstract: For real spaces, we show that being injected in a Hilbert space is a 3-space property. As a consequence, we obtain that, when does not carry a strictly positive Radon measure, every quadratic continuous homogeneous real-valued polynomial on 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

DOI:
https://doi.org/10.1090/S0002-9939-08-09574-9

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.