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Download QR code; Print/export Download as PDF; Printable version; In other projects ... This can be derived from the "only if" part of Krein's theorem above. [4]
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 Hahn–Banach theorem asserts that φ can be extended to a linear functional on V that is dominated by N. To derive this from the M. Riesz extension theorem, define a convex cone K ⊂ R×V by = {(,) ()}. Define a functional φ 1 on R×U by
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 other projects ... the Krein–Rutman theorem is a generalisation of the Perron–Frobenius theorem to infinite-dimensional ...
Krein extension theorem - a theorem in functional analysis, proved by the Soviet mathematician Mark Grigorievich Krein; M. Riesz extension theorem - a theorem in mathematics, proved by Marcel Riesz; Szpilrajn extension theorem - a theorem in set theory, proved by Edward Szpilrajn; Tietze extension theorem - a theorem in topology, named after ...
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Krein–Milman theorem; M. Monsky's theorem; R.
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 ...