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Ideals of finite rank operators, intersection properties of balls, and the approximation property

Åsvald Lima, Eve Oja (1999)

Studia Mathematica

We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of $c_{0}$ , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).

Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

Erhan Çalışkan (2007)

Czechoslovak Mathematical Journal

We show that a Banach space $E$ has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on $E$ can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.

Inner M-ideals in Banach algebras.

Wend Werner (1991)

Mathematische Annalen

Integral multilinear forms on $C (K, X)$ spaces

Ignacio Villanueva (2004)

Czechoslovak Mathematical Journal

We use polymeasures to characterize when a multilinear form defined on a product of $C (K, X)$ spaces is integral.

Integral operators on the section space of a Banach bundle.

Kitchen, J.W., Robbins, D.A. (1993)

International Journal of Mathematics and Mathematical Sciences

Isomorphic properties in spaces of compact operators

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

We introduce the definition of $p$ -limited completely continuous operators, $1 \leq p < \infty$ . The question of whether a space of operators has the property that every $p$ -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using $p$ -limited completely continuous evaluation operators.