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RESEARCH PRODUCT

Zeroes of real polynomials on C(K) spaces

Jesús Ferrer

subject

PolynomialFunction spaceApplied MathematicsC(K) spacesMathematical analysisHausdorff spaceContinuous polynomialsLinear subspaceZero-setSquare-free polynomialCombinatoricsCompact spaceCountable chain conditionHomogeneous polynomialAnalysisMathematics

description

AbstractFor a compact Hausdorff topological space K, we show that the function space C(K) must satisfy the following dichotomy: (i) either it admits a positive definite continuous 2-homogeneous real-valued polynomial, (ii) or every continuous 2-homogeneous real-valued polynomial vanishes in a non-separable closed linear subspace. Moreover, if K does not have the Countable Chain Condition, then every continuous polynomial, not necessarily homogeneous and with arbitrary degree, has constant value in an isometric copy of c0(Γ), for some uncountable Γ.

yearjournalcountryeditionlanguage
2007-12-01Journal of Mathematical Analysis and Applications
10.1016/j.jmaa.2007.02.083http://dx.doi.org/10.1016/j.jmaa.2007.02.083