Noncommutative measure and integration

Noncommutative measure and integration MSC classification 46L51. Because of the progress in the theory of von Neumann algebras and the expansion of its applications from 1966 to 1974 which was stimulated by the Tomita-Takesaki theory and the theory of normal weights, extending the noncommutative integration theory by Irving Ezra Segal has become important to normal weights being noncentral analogs to integrals by unbounded measures on the class of bounded functions.

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

Further reading

• Projections as noncommutative characteristic functions

References

• 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)
• "Handbook of quantum logic and quantum structures: quantum structures"; Kurt Engesser, Daniel Lehmann; Publisher Elsevier, 2007 ISBN 0444528709 [1]