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The precompactness-lemma. (English) Zbl 0599.46005
The purpose of this work is to draw attention to a result of Grothendieck which states that if \(<E,F>\) is a dual system, \(A\subset E\), \(B\subset F\), then \(B^ 0\)-precompactness of A is equivalent to \(A^ 0\)- precompactness of B. A more general version due to Kakutani is also discussed briefly. Some elegant examples are given to demonstrate the applicability of this lemma.

MSC:
46A20 Duality theory for topological vector spaces
46A50 Compactness in topological linear spaces; angelic spaces, etc.
46A32 Spaces of linear operators; topological tensor products; approximation properties
46G10 Vector-valued measures and integration
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