alaoglu造句
例句与造句
- 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.
- It's difficult to find alaoglu in a sentence. 用alaoglu造句挺难的
- A proof of this theorem for separable normed vector spaces was published in 1932 by Stefan Banach, and the first proof for the general case was published in 1940 by the mathematician Leonidas Alaoglu.
- 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.
- Alaoglu and ErdQs tabulated all highly abundant numbers up to 10 4, and showed that the number of highly abundant numbers less than any " N " is at least proportional to log 2 " N ".
- 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.
- Some of the notable mathematical concepts that bear Banach's name include Banach spaces, Banach algebras, the Banach Tarski paradox, the Hahn Banach theorem, the Banach Steinhaus theorem, the Banach-Mazur game, the Banach Alaoglu theorem, and the Banach fixed-point theorem.
- These include theorems about compactness of certain spaces such as the Banach Alaoglu theorem on the weak-* compactness of the unit ball of the dual space of a normed vector space, and the Arzel? Ascoli theorem characterizing the sequences of functions in which every subsequence has a cellular automata.
- Due to the constructive nature of its proof ( as opposed to the general case, which is based on the axiom of choice ), the sequential Banach Alaoglu theorem is often used in the field of partial differential equations to construct solutions to PDE or lower semi-continuity property in the weak * topology.