By Corneliu Constantinescu
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Additional resources for C* Algebras, Volume 2: Banach Algebras and Compact Operators
This is equivalent to saying that every such sequence S is, itself, relatively weakly compact, since S ∞∞ is the weak closure of a countable set of suitable rational linear combinations of points in S. Therefore, (ii) X is a P-space if and only if every bounded sequence in C p (X ) is relatively compact. The beautifully simple statements (i) and (ii) do not require any knowledge of the weak barrelledness that motivated them. Now Γ→ -barrelled ∗ property (C) ∗ property (S) ∗ dlc ∗ primitive, as Fig.
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Comment. Math. : A note on dual-separating F-spaces. Bull. Polish Acad. Sci. Math. : Some remarks on ∗ -Baire-like and on b-∗ -Baire-like spaces. Math. : On nonlocally convex and on dual-less separable topological vector spaces. : On suprema of metrizable vector topologies with trivial dual. Czech. Math. J. 36(111), no. : On bounded multiplier summable sequences in topological vector spaces. Math. Nachr. : On countable codimensional subspaces in ultra-(DF) spaces. Acta Math. Hung. : Nonlocally convex spaces and the Hahn-Banach extension property.
C* Algebras, Volume 2: Banach Algebras and Compact Operators by Corneliu Constantinescu