Duality results in Banach and quasi-Banach spaces of homogeneous polynomials and applications
Volume 240 / 2018
Studia Mathematica 240 (2018), 123-145
MSC: Primary 46A20, 46G20, 46A16; Secondary 46G25, 47A16.
DOI: 10.4064/sm8608-4-2017
Published online: 25 August 2017
Abstract
Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasi-norms instead of norms. In this paper we extend a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the dual of the space with the new norm coincides with the dual of the space with the original quasi-norm. Applications to problems on the existence and approximation of solutions of convolution equations and on hypercyclic convolution operators on spaces of entire functions are provided.
