The dual of the locally convex space \(C_p(X)\) (Q740793)
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scientific article; zbMATH DE number 6341731
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The dual of the locally convex space \(C_p(X)\) |
scientific article; zbMATH DE number 6341731 |
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The dual of the locally convex space \(C_p(X)\) (English)
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9 September 2014
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Let \(X\) denote an infinite Tikhonov space and \(C_p(X)\) the space of all continuous real-valued functions on \(X\) endowed with the topology of pointwise convergence. Furthermore, let \(L_p(X)\) be the topological dual \(L(X)\) of \(C_p(X)\) endowed with the weak topology \(\sigma(L(X),C_p(X))\). Depending on the topological properties of \(X\), the authors prove which of the fourteen standard weak barrelledness properties are satisfied by \(L_p(X)\).
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weak barrelledness
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\(P\)-spaces
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separable quotients
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