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• Von_Neumann_algebra abstract "In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries.Two basic examples of von Neumann algebras are as follows. The ring L∞(R) of essentially bounded measurable functions on the real line is a commutative von Neumann algebra, which acts by pointwise multiplication on the Hilbert space L2(R) of square integrable functions. The algebra B(H) of all bounded operators on a Hilbert space H is a von Neumann algebra, non-commutative if the Hilbert space has dimension at least 2. Von Neumann algebras were first studied by von Neumann (1929); he and Francis Murray developed the basic theory, under the original name of rings of operators, in a series of papers written in the 1930s and 1940s (F.J. Murray & J. von Neumann 1936, 1937, 1943; J. von Neumann 1938, 1940, 1943, 1949), reprinted in the collected works of von Neumann (1961).Introductory accounts of von Neumann algebras are given in the online notes of Jones (2003) and Wassermann (1991) and the books by Dixmier (1981), Schwartz (1967), Blackadar (2005) and Sakai (1971). The three volume work by Takesaki (1979) gives an encyclopedic account of the theory. The book by Connes (1994) discusses more advanced topics.".
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• Von_Neumann_algebra first "F.J.".
• Von_Neumann_algebra first "J.".
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• Von_Neumann_algebra id "V/v096900".
• Von_Neumann_algebra last "Murray".
• Von_Neumann_algebra last "Shtern".
• Von_Neumann_algebra last "von Neumann".
• Von_Neumann_algebra nb "yes".
• Von_Neumann_algebra title "von Neumann algebra".
• Von_Neumann_algebra year "1936".
• Von_Neumann_algebra year "1937".
• Von_Neumann_algebra year "1938".
• Von_Neumann_algebra year "1940".
• Von_Neumann_algebra year "1943".
• Von_Neumann_algebra year "1949".
• Von_Neumann_algebra subject Category:Operator_theory.
• Von_Neumann_algebra subject Category:Von_Neumann_algebras.
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• Von_Neumann_algebra type Algebra106012726.
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• Von_Neumann_algebra type PureMathematics106003682.
• Von_Neumann_algebra type Science105999797.
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• Von_Neumann_algebra comment "In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics.".
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• Von_Neumann_algebra label "Алгебра фон Неймана".
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