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

2008

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.

Sobre espacios cuasi-uniformes

1984