von Neumann algebra

mathematics

Also known as: W*-algebra, operator ring, ring of operators

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Von Neumann algebras are a class of algebraic structures in mathematics that are fundamental to the field of functional analysis. Developed by the brilliant mathematician John von Neumann, these algebras are collections of operators on a Hilbert space. They play a crucial role in the mathematical formulation of quantum mechanics, providing a rigorous framework for understanding quantum states and observables. Von Neumann's work in this area, alongside his other groundbreaking contributions to fields like game theory and computer science, solidified his reputation as one of the most influential mathematicians of the 20th century.12

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John von Neumann
Princeton, 1930–42
…of operators, now known as von Neumann algebras (1929 through the 1940s). Other achievements include a proof of the quasi-ergodic hypothesis (1932) and important work in lattice theory (1935–37). It was not only the new physics that commanded von Neumann’s attention. A 1932 Princeton lecture, “On Certain Equations of Economics…
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…of operators, now known as von Neumann algebras (1929 through the 1940s). Other achievements include a proof of the quasi-ergodic hypothesis (1932) and important work in lattice theory (1935–37). It was not only the new physics that commanded von Neumann’s attention. A 1932 Princeton lecture, “On Certain Equations of Economics…
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Vaughan Jones
In his study of von Neumann algebras (algebras of bounded operators acting on a Hilbert space), Jones came across polynomials that were invariant for knots and links—simple closed curves in three-dimensional space. Initially it was suspected that these were essentially Alexander polynomials (named after the work of the American…
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In his study of von Neumann algebras (algebras of bounded operators acting on a Hilbert space), Jones came across polynomials that were invariant for knots and links—simple closed curves in three-dimensional space. Initially it was suspected that these were essentially Alexander polynomials (named after the work of the American…
Read More