approximation problem - Wolfram|Alpha

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Input interpretation

approximation problem

Definition

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

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Related terms

approximation property | Banach space | compact operator

Subject classifications

MathWorld

functional analysis | spaces

MSC 2010

46-XX | 54Axx

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