Approximation Problem
المؤلف:
Enflo, P.
المصدر:
"A Counterexample to the Approximation Problem in Banach Spaces." Acta Math. 130
الجزء والصفحة:
...
31-7-2021
1713
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.
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