Search results
Results From The WOW.Com Content Network
Krein-Smulian Theorem: [2] — Let be a Banach space and a weakly compact subset of (that is, is compact when is endowed with the weak topology). Then the closed convex hull of K {\displaystyle K} in X {\displaystyle X} is weakly compact.
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 .
to be dense in a weighted L 2 space on the real line. It was discovered by Mark Krein in the 1940s. [1] A corollary, also called Krein's condition, provides a sufficient condition for the indeterminacy of the moment problem. [2] [3]
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 ...
The definition of the Friedrichs extension is based on the theory of closed positive forms on Hilbert spaces. If T is non-negative, then (,) = + is a sesquilinear form on dom T and
The Krein–Milman theorem is arguably one of the most well-known theorems about extreme points. Krein–Milman theorem — If S {\displaystyle S} is convex and compact in a locally convex topological vector space , then S {\displaystyle S} is the closed convex hull of its extreme points: In particular, such a set has extreme points.
In functional analysis, the Krein–Rutman theorem is a generalisation of the Perron–Frobenius theorem to infinite-dimensional Banach spaces. [1] It was proved by Krein and Rutman in 1948. [ 2 ]
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.