Search results
Results From The WOW.Com Content Network
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 .
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.
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.
The original Krein–Milman theorem follows from Choquet's result. Another corollary is the Riesz representation theorem for states on the continuous functions on a metrizable compact Hausdorff space. More generally, for V a locally convex topological vector space, the Choquet–Bishop–de Leeuw theorem [1] gives the same formal statement.
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 ]
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Help; Learn to edit; Community portal; Recent changes; Upload file
Theorem — The set of states of a -algebra with a unit element is a compact convex set under the weak-topology. In general, (regardless of whether or not A {\displaystyle A} has a unit element) the set of positive functionals of norm ≤ 1 {\displaystyle \leq 1} is a compact convex set.