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John von Neumann and the Theory of Operator Algebras (1995) [2 citations — 2 self]

by Dénes Petz ,  Miklós Rédei
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Abstract:

After some earlier work on single operators, Von Neumann turned to families of operators in [1]... or algebra theory is neither entirely historical nor is it complete. It reflects the scientific taste and knowledge of the authors. The theory of operator algebras is a technical subject and to present a readable account of the development of many years is a difficult task. To facilitate reading, each section begins with an informal review of the essential ideas discussed in the section.

Citations

270 Operator Algebras and Quantum Statistical Mechanics 2. Second edition – Bratteli, Robinson - 1997
59 Measures on the closed subspaces of a Hilbert space – Gleason - 1957
46 Tomita’s theory of modular Hilbert algebras and its applications. Lecture – Takesaki
32 Index for subfactors, Invent – Jones - 1983
27 Algebraic Methods in Statistical Mechanics and Quantum Field Theory – Emch - 1972
22 Local quantum physics. Fields, particles, algebras. Second edition. Texts and Monographs in Physics – Haag - 1996
20 On rings of operators – Murray, Neumann - 1943
15 Connes' bicentralizer problem and uniqueness of injective factors of type III1 – Haagerup - 1987
12 A non-commutative extension of abstract integration – Segal - 1953
12 Bogoliubov automorphisms and Fock representations of canonical anticommutation relations – Araki - 1987
10 On an algebraic generalization of the quantum mechanical formalism – Jordan, Neumann, et al. - 1934
10 An invitation to the algebra of the canonical commutation relation – Petz - 1990
4 Zur Algebra der Funktionaloperatoren und Theorie der normalen – Neumann - 1929
4 On algebraic generalization of the quantum mechanical formalism – Neumann - 1936
4 On the independence of local algebras in quantum theory – Summers - 1990
3 The uniqueness of Haar's measure – Neumann - 1936
3 Index theory for operator algebras – Kosaki - 1991
3 The work of Vaughan F.R – Birman - 1992
3 The work of Alain Connes – Araki - 1997
3 operator algebras – Hanche-Olsen, Strmer, et al. - 1984
3 On the imbedding of normed rings into the ring of operators in Hilbert space – Gelfand, Naimark - 1943
3 Die Eindeutigkeit des Schrödingerschen Operatoren – Neumann - 1931
3 An algebraic approach to quantum theory – Haag, Kastler - 1964
2 Ma Begri in der Theorie der kontinuierlichen Gruppen – Haar, Der - 1959
2 On ergodic and the isomorphism of factors – Krieger - 1976
2 Une classi des facteurs de type – Connes - 1973
2 On factor representations and the C*-algebra of canonical commutation relations – Slawny
1 Zum Haarschen Ma – Neumann
1 Extensions of Gleason theorem, in Quantum Probability and Applications to the Quantum Theory of Irreversible Processes – Kruszinsky
1 On the equilibrium states – Haag, Hugenholz, et al.
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