Zeros of polynomials on Banach spaces: the real story

Source: https://www.maths.tcd.ie/report_series/abstracts/tcdm0103.html Parent: https://www.maths.tcd.ie/research/papers/

Zeros of polynomials on Banach spaces: the real story

Let E be a real Banach space. We show that either E has a positive definite 2-homogeneous polynomial or every 2-homogeneous polynomial on E vanishes on an infinite dimensional subspace of E. Under additional assumptions, we show that such subspaces are non-separable.