6533b828fe1ef96bd1287879

RESEARCH PRODUCT

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

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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.