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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.

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