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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.
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 mathematical analysis, Krein's condition provides a necessary and sufficient condition for exponential sums {= (),,},to be dense in a weighted L 2 space on the real line.
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, a credal set is a set of probability distributions [1] or, more generally, a set of (possibly only finitely additive) probability measures.A credal set is often assumed or constructed to be a closed convex set.
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 .
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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.