Mark Krein is a prominent mathematician known for his contributions to functional analysis, operator theory, and related fields. His work involves the study of Krein spaces, which are a type of inner product space that can accommodate indefinite inner products, leading to various applications in mathematical physics and other areas. Krein is noteworthy for his influence in the areas of spectral theory, linear operators, and the investigation of linear systems.
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Mark Krein was a mathematician whose research joined functional analysis, operator theory, harmonic analysis and mathematical physics. He worked on the moment problem, integral equations and the spectral theory of linear operators, building an influential research school despite severe institutional discrimination.[ref]
https://mathshistory.st-andrews.ac.uk/Biographies/Krein/. Biography, research on moments and operators, Odessa school and dismissals
The Krein-Milman theorem, proved with David Milman, gives a geometric expression of this work: a nonempty compact convex set in a locally convex Hausdorff space is the closed convex hull of its extreme points. In finite dimensions, the corresponding picture is a convex polygon reconstructed from its vertices.
Portrait of Mark Krein
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