alaoglu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.
- Conversely, every bounded sequence in a Hilbert space admits weakly convergent subsequences ( Alaoglu's theorem ).
- Alaoglu and ErdQs's conjecture remains open, although it has been checked up to at least 10 7.
- 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.
- Unknown to Alaoglu and ErdQs, about 30 pages of Ramanujan's 1915 paper " Highly Composite Numbers " were suppressed.
- 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.
- It's difficult to see alaoglu in a sentence. 用alaoglu造句挺难的
- In their 1944 paper, Alaoglu and ErdQs conjectured that the ratio of two consecutive colossally abundant numbers was always a prime number.
- Alaoglu and ErdQs noted that all superabundant numbers are highly abundant, and asked whether there are infinitely many highly abundant numbers that are not superabundant.
- 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.
- Alaoglu and ErdQs's conjecture would also mean that no value of ? gives four different integers " n " as maxima of the above function.
- Non-separable Banach spaces cannot embed isometrically in the separable space, but for every Banach space, one can find a Banach & ndash; Alaoglu theorem.
- A special case of the conjecture is mentioned in a 1944 paper of Leonidas Alaoglu and Paul ErdQs who suggest that it had been considered by Carl Ludwig Siegel.
- Alaoglu and ErdQs studied how many different values of " n " could give the same maximal value of the above function for a given value of ?.
- Alaoglu's theorem states that if " E " is a topological vector space, then every equicontinuous subset of " E * " is weak-* relatively compact.