Plank type problems for polynomials on Banach spaces

In this work we prove plank type problems for polynomials on Banach spaces. We give estimates in the case of complex Banach spaces and in particular in the case of complex Hilbert spaces. Moreover, we get optimal results in the case of 2-homogeneous polynomials on real Hilbert spaces. We have also derived estimates in the case of the classical L p ( μ ) spaces.