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The lattice structure of C*-algebras and their duals

Published online by Cambridge University Press:  24 October 2008

Michael D. Green
Michael D. Green
Affiliation:
School of Mathematics, The University, Newcastle upon Tyne, NEI 7RU
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Extract

Let A be a *-algebra of operators on a Hilbert space H, and let Ah, A+ denote respectively the sets of self-adjoint and positive operators in A. A+ is a positive cone in Ah and it induces a partial ordering in Ah. The lattice properties of Ah were studied by R. Archbold in (1) and (2), and Chu Cho-Ho gave a different proof of some of his results in (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 2 , March 1977 , pp. 245 - 248
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Archbold, R.Prime C*-algebras and antilattices. Proc. London Math. Soc. 24 (1972), 669–680.CrossRefGoogle Scholar
(2)Archbold, R.Order and commutativity in C*-algebras. Proc. Cambridge Philos. Soc. 76 (1972), 153–155.CrossRefGoogle Scholar
(3)Chu, Cho-Ho. Prime faces in C*-algebras. J. London Math. Soc. 7 (1973), 175–180.Google Scholar
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