Approximation properties determined by operator ideals and approximability of homogeneous polynomials and holomorphic functions
Volume 208 / 2012
Studia Mathematica 208 (2012), 97-116
MSC: Primary 46G25; Secondary 46G20, 46B28, 47B10.
DOI: 10.4064/sm208-2-1
Abstract
Given an operator ideal $\cal I$, a Banach space $E$ has the $\cal I$-approximation property if the identity operator on $E$ can be uniformly approximated on compact subsets of $E$ by operators belonging to $\cal I$. In this paper the $\cal I$-approximation property is studied in projective tensor products, spaces of linear functionals, spaces of linear operators/homogeneous polynomials, spaces of holomorphic functions and their preduals.
