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Jochen Wengenroth
Jochen Wengenroth
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It is well-known that a Hausdorff locally convex space is semi-reflexive (i.e., the canonical map into its bidual is surjective) if and only if every weakly closed bounded set is weakly compact. This is proposition 23.18 in Introduction to Functional Analysis of Meise and Vogt.

(It is mainly a consequence of Alaoglu's theorem.)

It is well-known that a Hausdorff locally convex space is semi-reflexive (i.e., the canonical map into its bidual is surjective) if and only if every closed bounded set is weakly compact. This is proposition 23.18 in Introduction to Functional Analysis of Meise and Vogt.

(It is mainly a consequence of Alaoglu's theorem.)

It is well-known that a Hausdorff locally convex space is semi-reflexive (i.e., the canonical map into its bidual is surjective) if and only if every weakly closed bounded set is weakly compact. This is proposition 23.18 in Introduction to Functional Analysis of Meise and Vogt.

(It is mainly a consequence of Alaoglu's theorem.)

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Jochen Wengenroth
Jochen Wengenroth
  • 16.4k
  • 2
  • 42
  • 82

It is well-known that a Hausdorff locally convex space is semi-reflexive (i.e., the canonical map into its bidual is surjective) if and only if every closed bounded set is weakly compact. This is proposition 23.18 in Introduction to Functional Analysis of Meise and Vogt.

(It is mainly a consequence of Alaoglu's theorem.)