| 释义 |
Operator ring
英语百科
Von Neumann algebra （重定向自Operator ring）
von Neumann, J. (1930), "Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren", Math. Ann. 102 (1): 370–427, doi:10.1007/BF01782352 . The original paper on von Neumann algebras.
von Neumann, J. (1936), "On a Certain Topology for Rings of Operators", Annals of Mathematics, Second Series 37 (1): 111–115, doi:10.2307/1968692, JSTOR 1968692 . This defines the ultrastrong topology.
von Neumann, J. (1938), "On infinite direct products", Compos. Math. 6: 1–77 . This discusses infinite tensor products of Hilbert spaces and the algebras acting on them.
von Neumann, J. (1940), "On rings of operators III", Annals of Mathematics, Second Series 41 (1): 94–161, doi:10.2307/1968823, JSTOR 1968823 . This shows the existence of factors of type III.
von Neumann, J. (1943), "On Some Algebraical Properties of Operator Rings", Annals of Mathematics, Second Series 44 (4): 709–715, doi:10.2307/1969106, JSTOR 1969106 . This shows that some apparently topological properties in von Neumann algebras can be defined purely algebraically.
von Neumann, J. (1949), "On Rings of Operators. Reduction Theory", Annals of Mathematics, Second Series 50 (2): 401–485, doi:10.2307/1969463, JSTOR 1969463 . This discusses how to write a von Neumann algebra as a sum or integral of factors.
von Neumann, John (1961), Taub, A.H., ed., Collected Works, Volume III: Rings of Operators, NY: Pergamon Press . Reprints von Neumann's papers on von Neumann algebras.
Wassermann, A. J. (1991), Operators on Hilbert space
| Authority control |
- GND: 4388395-3
- NDL: 00574108
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