A variant of Grothendieck's theorem on weak* convergent sequences (Q1901989)
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scientific article; zbMATH DE number 815710
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A variant of Grothendieck's theorem on weak* convergent sequences |
scientific article; zbMATH DE number 815710 |
Statements
A variant of Grothendieck's theorem on weak* convergent sequences (English)
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9 February 1997
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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 \(C(K)\).
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space of continuous functions
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weak* convergence
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compact quasi-Stonian space
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sequentially order continuous linear functionals
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