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Krein–Milman theorem [2] — Suppose is a Hausdorff locally convex topological vector space (for example, a normed space) and is a compact and convex subset of . Then K {\displaystyle K} is equal to the closed convex hull of its extreme points : K = co ¯ ( extreme ( K ) ) . {\displaystyle K~=~{\overline {\operatorname {co ...
In mathematics, particularly in functional analysis, the Krein-Smulian theorem can refer to two theorems relating the closed convex hull and compactness in the weak topology. They are named after Mark Krein and Vitold Shmulyan , who published them in 1940.
Download as PDF; Printable version; ... In mathematical analysis, Krein's condition provides a ... This can be derived from the "only if" part of Krein's theorem ...
Nielsen–Schreier theorem (free groups) Orbit-stabilizer theorem (group theory) Schreier refinement theorem (group theory) Schur's lemma (representation theory) Schur–Zassenhaus theorem (group theory) Sela's theorem (hyperbolic groups) Stallings theorem about ends of groups (group theory) Superrigidity theorem (algebraic groups)
Mark Grigorievich Krein (Ukrainian: Марко́ Григо́рович Крейн, Russian: Марк Григо́рьевич Крейн; 3 April 1907 – 17 October 1989) was a Soviet mathematician, one of the major figures of the Soviet school of functional analysis.
Let be a Banach space, and let be a convex cone such that = {}, and is dense in , i.e. the closure of the set {:,} =. is also known as a total cone.Let : be a non-zero compact operator, and assume that it is positive, meaning that (), and that its spectral radius is strictly positive.
In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is a natural extension of Pontryagin duality , between compact and discrete commutative topological groups, to groups that are compact but noncommutative .
Carathéodory's existence theorem; Cartan–Kähler theorem; Cartan–Kuranishi prolongation theorem; Cauchy formula for repeated integration; Cauchy–Kovalevskaya theorem; Chain rule; Chaplygin's theorem; Chebyshev–Markov–Stieltjes inequalities; Conformal welding; Conley–Zehnder theorem