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Introduction to Von Neumann Algebras and Continuous Geometry

Published online by Cambridge University Press:  20 November 2018

Israel Halperin
Israel Halperin*
Affiliation:
Queen's University
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What is a von Neumann algebra? What is a factor (i) of type I, (ii) of type II, (iii) of type III? What is a projection geometry? And finally, what is a continuous geometry?

The questions recall some of the most brilliant mathematical work of the past 30 years, work which was done by John von Neumann, partly in collaboration with F. J. Murray, and which grew out of von Neumann1 s analysis of linear operators in Hilbert space.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 3 , 01 September 1960 , pp. 273 - 288
Copyright
Copyright © Canadian Mathematical Society 1960

References

. Amemiya, I. and Halperin, I., Complemented modular lattices, Canad. J. Math. 11 (1959), 481-520.Google Scholar
2. Dixmier, J., Lesalgèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann), Gauthier-Villars, Paris, 1957.Google Scholar
3. Irving, Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math. 61 (1955), 524-541.Google Scholar
4. von Neumann, J., Allgemeine Eigenwerttheorie hermitescher Funktionaloperatoren, Math. Ann. 102 (1929), 49-131.Google Scholar
5. von Neumann, J., Zur Algebra der Funktionaloperatoren und Theorie der normalen Operatoren, Math. Ann. 102 (1929), 370-427.Google Scholar
6. von Neumann, J., On a certain topology for rings of operators, Ann. of Math. 37 (1936), 111-115.Google Scholar
7. Murray, F. J. and von Neumann, J., On rings of operators, Ann. of Math. 37 (1936), 116-229.Google Scholar
8. von Neumann, J., On infinite direct products, Compositio Math. 6 (1938), 1-77.Google Scholar
9. von Neumann, J., On rings of operators, III, Ann, of Math. 41 (1940), 94-161.Google Scholar
10. Murray, F. J.andvon Neumann, J., On rings of operators, IV, Ann.of Math. 44 (1943), 716-808.Google Scholar
11. von Neumann, J., On some algebraical properties of operatorrings, Ann. of Math. 44 (1943), 709-715.Google Scholar
12. von Neumann, J., On rings of operators. Reduction theory, Ann. of Math. (1949), 401-485.Google Scholar
13. von Neumann, J., 5 Notes in Proc. Nat. Acad. Sci. U.S.A., 1936-37, and Continuous Geometry, mimeographed lecture notes, The Institute for Advanced Study, Princeton, 1935-37, published by Princeton University Press, 1960.Google Scholar
14. Loomis, L. H., The lattice theoretic background of the dimension theory, Mem. Amer. Math. Soc. (1955).Google Scholar
15. Maeda, S., Dimension functions on certain general lattices, J.Sci. Hiroshima Univ. 19 (1955), 211-237.Google Scholar