Projecting Lipschitz Functions Onto Spaces of Polynomials

The Banach space $$\mathcal {P}({}^2X)$$ of 2-homogeneous polynomials on the X can be naturally embedded in $${\mathrm{Lip}_0}(B_X)$$ real-valued Lipschitz functions $$B_X$$ that vanish at 0. We investigate whether is a complemented subspace . This line research considered as polynomial counterpart to classical result by Joram Lindenstrauss, asserting {P}({}^1X)=X^*$$ for every X. Our main asserts not with non-trivial type.