Complexifications of real Banach spaces, polynomials and multilinear maps
Volume 134 / 1999
Studia Mathematica 134 (1999), 1-33
DOI: 10.4064/sm-134-1-1-33
Abstract
We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.
