POLARIZATION CONSTANTS OF POLYNOMIALS ON BANACH SPACES

Abstract

If L is a continuous symmetric n-linear form on a real or complex Banach space and bL is the associated continuous n-homogeneous polynomial, then |bL| leq |b| leq n^n/n!|bl|. However, the right hand inequality can be tightened for many Banach spaces. In this work we discuss this problem and we give some optimal constants as well as some new simple proofs to known results. Many other related problems have been discussed and some interesting open questions have been posed.