Approximation properties determined by operator ideals

2010/09/15 by Sonia Berrios, Geraldo Botelho, Berrios, Sonia +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1009.2977

Abstract

Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in projective tensor products, spaces of linear functionals, spaces of homogeneous polynomials (in particular, spaces of linear operators), spaces of holomorphic functions and their preduals.

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• Polynomial ideals from a nonlinear viewpoint

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