Noncommutative measure and integration

Noncommutative measure and integration refers to the theory of weights, states, and traces on von Neumann algebras (Takesaki 1979 v. 2 p. 141). The MSC classification of the field is 46L51.

History

The original paper on noncommutative measure and integration theory in 1951 led to the Plancherel theorem for noncommutative locally compact groups.

See also

• List of noncommutative topics in mathematics

References

• "Handbook of quantum logic and quantum structures: quantum structures"; Kurt Engesser, Daniel Lehmann; Publisher Elsevier, 2007 ISBN 0444528709 [1]
• I. E. Segal. A noncommutative extension of abstract integration. Ann. of Math. (2), 57:401–457, 1953. MR # 14:991f, JSTOR collection. 2.0(2)
• Takesaki, M. (1979), Theory of Operator Algebras I, II, III, ISBN 3-540-42248-X ISBN 3-540-42914-X ISBN 3-540-42913-1 {{citation}}: Check |isbn= value: invalid character (help)

External links

• "Operator algebras and their applications," Kazan State University.
• Projections as noncommutative characteristic functions, PlanetMath