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Noncommutative Lp-spaces with 0 < p < 1

Published online by Cambridge University Press:  24 October 2008

Kichi-Suke Saito
Kichi-Suke Saito
Affiliation:
Niigata University, Niigata, 950–21, Japan
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Extract

The noncommutative Lp-spaces (1 ≤ p ≤ ∞) of unbounded operators associated with a regular gauge space (a von Neumann algebra equipped with a faithful normal semifinite trace) are studied by many authors ((4), (5) and (7)). It is well-known that the noncommutative Lp-spaces (1 ≤ P < ∞) are Banach spaces and the dual of Lp is Lq (1 ≤ p < ∞, 1/p + 1/q = 1) by means of a Radon-Nikodym theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 3 , May 1981 , pp. 405 - 411
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

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