alaoglu theorem造句
例句与造句
- Its importance comes from the Banach Alaoglu theorem.
- The Banach Alaoglu theorem depends on Tychonoff's theorem about infinite products of compact spaces.
- Under the weak topology the bounded sets coincide with the relatively compact sets which leads to the important Bourbaki Alaoglu theorem.
- The weak operator topology is useful for compactness arguments, because the unit ball is compact by the Banach-Alaoglu theorem.
- The "'Bourbaki Alaoglu theorem "'is a generalization by Bourbaki to dual topologies on locally convex spaces.
- It's difficult to find alaoglu theorem in a sentence. 用alaoglu theorem造句挺难的
- Consequently, for normed vector space ( and hence Banach spaces ) the Bourbaki Alaoglu theorem is equivalent to the Banach Alaoglu theorem.
- Consequently, for normed vector space ( and hence Banach spaces ) the Bourbaki Alaoglu theorem is equivalent to the Banach Alaoglu theorem.
- Since the Banach Alaoglu theorem is proven via Tychonoff's theorem, it relies on the ZFC axiomatic framework, in particular the axiom of choice.
- By the Banach Alaoglu theorem and the reflexivity of " H ", the closed unit ball " B " is weakly compact.
- It should be cautioned that despite appearances, the Banach Alaoglu theorem does " not " imply that the weak-* topology is locally compact.
- Non-separable Banach spaces cannot embed isometrically in the separable space, but for every Banach space, one can find a Banach & ndash; Alaoglu theorem.
- An important fact about the weak * topology is the Banach Alaoglu theorem : if " X " is normed, then the closed unit ball in " X * " is weak *-reflexive.
- The Delta-compactness theorem is similar to the Banach Alaoglu theorem for weak convergence but, unlike the Banach-Alaoglu theorem ( in the non-separable case ) its proof does not depend on the Axiom of Choice.
- The Delta-compactness theorem is similar to the Banach Alaoglu theorem for weak convergence but, unlike the Banach-Alaoglu theorem ( in the non-separable case ) its proof does not depend on the Axiom of Choice.
- The Axiom of Choice is equivalent to a fundamental result of point-set topology, Tychonoff's theorem, and also to the conjunction of two fundamental results of functional analysis, the Banach Alaoglu theorem and the Krein Milman theorem.
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