Alaoglu

Leonidas Alaoglu
... Leonidas Alaoglu (March 19, 1914 – August 1981) was a Canadian-American mathematician, most famous for his widely-cited result called Alaoglu's theorem on the weak-star ...

Leonidas Alaoglu - Life and Work
... Alaoglu was born in Red Deer, Alberta to Greek parents ... His doctoral thesis is the source of Alaoglu's theorem ... The Bourbaki–Alaoglu theorem is a generalization of this result by Bourbaki to dual topologies ...

Sequential Banach–Alaoglu Theorem
... A special case of the Banach–Alaoglu theorem is the sequential version of the theorem, which asserts that the closed unit ball of the dual space of a separable normed vector space is sequentially ... 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 variational problems ... a minimizing sequence    which approaches the infimum of F, use the sequential Banach–Alaoglu theorem to extract a subsequence that converges in the weak* topology to a ...

Banach–Alaoglu Theorem - Generalization: Bourbaki–Alaoglu Theorem
... The Bourbaki–Alaoglu theorem is a generalization by Bourbaki to dual topologies ... for normed vector space (and hence Banach spaces) the Bourbaki–Alaoglu theorem is equivalent to the Banach–Alaoglu theorem ...

Banach–Alaoglu Theorem
... In functional analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of a normed vector space is compact in the ... first proof for the general case was published in 1940 by the mathematician Leonidas Alaoglu ... Since the Banach–Alaoglu theorem is proven via Tychonoff's theorem, it relies on the ZFC axiomatic framework, in particular the axiom of choice ...