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

Ferrer, Jesús

doi:10.1090/S0002-9939-08-09574-9

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