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A variant of Grothendieck’s theorem on weak* convergent sequences. (English) Zbl 0855.46018

The authors give a new proof of the following theorem: Let \(K\) be a compact quasi-Stonian space. Then every \(\sigma (C(K)^*, C(K))\)-compact subset of \(C(K)^*_c\) is also \(\sigma (C(K)^*, C(K)^{**})\)-compact. Hereby \(C(K)^*_c\) denotes the space of all sequentially order continuous linear functionals on \(C(K)\).
Reviewer: H.Weber (Udine)

MSC:

46E15 Banach spaces of continuous, differentiable or analytic functions
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References:

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