Approximation Problem

The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator  from a Banach space  to a Banach space  is the uniform operator topology of a sequence of operators with finite rank. This question was answered in the negative by Enflo (1973), who provided a deep counterexample to this problem.

REFERENCES:

Enflo, P. "A Counterexample to the Approximation Problem in Banach Spaces." Acta Math. 130, 309-317, 1973.

Grothendieck, A. Produits tensoriels topologiques et espaces nucléaires. Providence, RI: Amer. Math. Soc., 1955.