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arXiv · 1503.01079

Duality results in Banach and quasi-Banach spaces of homogeneous polynomials and applications

V. V. Favaro·D. Pellegrino
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Abstract

Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasinorms instead of norms. In this paper we develop 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.

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V. V. Favaro, D. Pellegrino. 2015-03-03. Duality results in Banach and quasi-Banach spaces of homogeneous polynomials and applications. https://doi.org/10.4064/sm8608-4-2017

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