Abstract
We consider the question: is every compact set in a Banach space X contained in the closed unit range of a compact (or even approximable) operator on X? We give large classes of spaces where the question has an affirmative answer, but observe that it has a negative answer, in general, for approximable operators. We further construct a Banach space failing the bounded compact approximation property, though all of its duals have the metric compact approximation property.
Publisher
Cambridge University Press (CUP)
Reference19 articles.
1. The Schwartz Hilbert variety;Bellenot;Michigan Math. J.,1975
2. A characterization of subspaces X and lp for which K(X) is an M-ideai in L(X);Cho;Proc. Amer. Math. Soc.,1985
3. Produits tensoriels topologies et espaces nucléates;Grothendieck;Mem. Amer. Math. Soc.,1955
4. Classical Banach Spaces I
5. Bounded approximate identities in the algebra of compact operators on a Banach space
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