Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T03:20:37.396Z Has data issue: false hasContentIssue false

Convergence of measurable operators

Published online by Cambridge University Press:  24 October 2008

F. J. Yeadon
Affiliation:
University of Hull

Extract

Segal(4) defines the algebra of measurable operators affiliated with a von Neumann algebra, and convergence nearly everywhere of a sequence of measurable operators, and shows that addition is jointly sequentially continuous and multiplication separately sequentially continuous in the star topology associated with convergence nearly everywhere.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Dunford, N. and Schwartz, J. T.Linear Operators Vol. ii. Interseience, New York, 1963.Google Scholar
(2)Sankaran, S.The *-algebra of unbounded operators. J. London Math. Soc. 34 (1959), 337344.CrossRefGoogle Scholar
(3)Sankaran, S.Stochastic convergence for operators. Quart. J. Math. Oxford Ser. 2 15 (1964), 97102.CrossRefGoogle Scholar
(4)Segai, I. E.A non-commutative extension of abstract integration. Ann. of Math. 57 (1953), 401457.Google Scholar
(5)Stinespring, W. F.Integration theorems for gages and duality for unimodular groups. Trans. Amer. Math. Soc. 90, (1959), 1556.CrossRefGoogle Scholar