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

Author(s): Jesús Ferrer
Journal: Proc. Amer. Math. Soc. 137 (2009), 573-577.
MSC (2000): Primary 47H60, 46B26
Posted: August 19, 2008
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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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T. Banakh, A. Plichko, A. Zagorodnyuk, Zeros of quadratic functionals on non-separable spaces, Colloq. Math. 100, No. 1 (2004), pp. 141-147. MR 2079354 (2005g:46047)

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J. Ferrer, On the zero-set of real polynomials in non-separable Banach spaces, Publ. of R.I.M.S. 43, No. 3 (2007), pp. 685-697. MR 2361792

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J. Ferrer, Zeroes of real polynomials on $ C(K)$ spaces, J. Math. Anal. Appl. 336 (2007), pp. 788-796. MR 2352980

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N. J. Kalton, N. T. Peck, Twisted sums of sequence spaces and the three-space problem, Trans. Amer. Math. Soc. 255 (1979), pp. 1-30. MR 542869 (82g:46021)

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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: 10.1090/S0002-9939-08-09574-9
PII: S 0002-9939(08)09574-9
Keywords: Quadratic polynomials, zero-set, $C(K)$ spaces
Received by editor(s): January 23, 2008
Posted: August 19, 2008
Additional Notes: The author has been partially supported by MEC and FEDER Project MTM2005-08210
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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