# 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.