Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-15T10:27:05.429Z Has data issue: false hasContentIssue false

Averaging operators in non commutative Lp spaces II

Published online by Cambridge University Press:  18 May 2009

C. Barnett
Affiliation:
Department Of Mathematics, Bedford College, London NW1 4NS
I. F. Wilde
Affiliation:
Department Of Mathematics, Bedford College, London NW1 4NS
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is the sequel to [1]. Briefly, the context in which we shall work is as follows. Let A b e a finite von Neumann algebra acting on a Hilbert space H. Let φ be a faithful normal finite trace on A with φ(I) = 1, where I is the identity of A. For 1<p<∞, let Lp(A) denote the non commutative Lebsegue spaces associated with (A, φ) [9].

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Barnett, C.. Averaging operators in non commutative Lp spaces I Glasgow Math. J. 24 (1983), 7174.CrossRefGoogle Scholar
2.Dunford, N. and Schwartz, J. T., Linear operators Part 1 (Interscience, 1958).Google Scholar
3.Dunford, N. and Schwartz, J. T., Linear operators Part 2 (Interscience, 1963).Google Scholar
4.Kelley, J. L.. Averaging operators in C∞(X), Illinois J. Math. 2 (1958), 214223.CrossRefGoogle Scholar
5.Kunze, R. A.. Lp Fourier transforms on locally compact unimodular groups, Trans. Amer. Math. Soc. 89 (1958), 519540.Google Scholar
6.Neveu, J.. Discrete parameter martingales. (North Holland, 1975).Google Scholar
7.Takesaki, M.. Theory of operator algebras I. (Springer-Verlag, 1979).CrossRefGoogle Scholar
8.Umegaki, H.. Conditional expectation in an operator algebra Tohoku Math. J. 6 (1954), 177181.CrossRefGoogle Scholar
9.Yeadon, F. J.. Non commutative Lp Spaces, Math. Proc. Cambridge Philos. Soc. 77 (1975), 91102.CrossRefGoogle Scholar
10.Yeadon, F. J.. Ergodic theorems for semifinite von Neumann algebras I. J. London Math. Soc. (2) 16 (1977), 326332.CrossRefGoogle Scholar