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.References
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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