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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.
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 ...
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 ...
Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Kirchberger's theorem; Krein–Milman theorem; M.
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.
Download as PDF; Printable version; In other projects ... Kolmogorov–Arnold representation theorem; Krein's condition; L. ... Wirtinger's representation and ...
Krein space Krein's condition Krein's extension theorem Krein–Milman theorem Krein–Rutman theorem Krein–Smulian theorem Akhiezer–Krein–Favard constant Markov–Krein theorem Tannaka–Krein duality: Awards: Wolf Prize (1982) Scientific career: Fields: Operator theory Mathematical Physics: Institutions: I.I. Mechnikov Odesa National ...
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.