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Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pOinted out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators a. ffiliated to such rings. The absence of power tools in functional analysis - mainly settled in their definitive form by A. Grothendieck around 1950-195- together with the pathological manipulation of algebraic operations on closed operators in Hilbert spaces, has limited ring-theory to the study of algebras of bounded operators with the main objective the difficult question of classifica tion up to isomorphisms of factors. This material has permitted a rigorous study of discrete systems in statistical mechanics but appears to be less convincing in other domains of physics (in the algebraic approach to field theory, for example). The striking role of Hamiltonians, Schrodinger operators and Lie group invariant properties in such areas of physics disappears in the so called C*-approach.
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Contenuti
Examples and Observations.- 1: Main Spaces.- 2: Density Theorems.- 3: Technical Properties of the Domain.- 4: Elementary Operations.- 5: Gelfand Transformation.- 6: Cofinal Central Systems and Derivations.- 7: Notion of Representation: The G.N.S. Case.- 8: The State Space.- 9: G-Invariance and G-Traces.- 10: Other Commutation Theorems.- 11: On Strong and Ultrastrong Topologies.- References.
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- EditoreD Reidel Pub Co
- Data di pubblicazione1985
- ISBN 10 9027718156
- ISBN 13 9789027718150
- RilegaturaCopertina rigida
- LinguaInglese
- Numero di pagine216
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Unbounded Non-Commutative Integration (Mathematical Physics Studies, 7)
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Unbounded Non-Commutative Integration
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Springer Netherlands Jun 1985, 1985
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ISBN 13: 9789027718150
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pOinted out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators a. ffiliated to such rings. The absence of power tools in functional analysis - mainly settled in their definitive form by A. Grothendieck around 1950-195- together with the pathological manipulation of algebraic operations on closed operators in Hilbert spaces, has limited ring-theory to the study of algebras of bounded operators with the main objective the difficult question of classifica tion up to isomorphisms of factors. This material has permitted a rigorous study of discrete systems in statistical mechanics but appears to be less convincing in other domains of physics (in the algebraic approach to field theory, for example). The striking role of Hamiltonians, Schrodinger operators and Lie group invariant properties in such areas of physics disappears in the so called C\*-approach. 216 pp. Englisch. Codice articolo 9789027718150
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Unbounded Non-Commutative Integration (Mathematical Physics Studies, 7)
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Unbounded Non-Commutative Integration
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical. Codice articolo 5814981
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Unbounded Non-Commutative Integration
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Springer Netherlands, Springer Netherlands, 1985
ISBN 10: 9027718156
ISBN 13: 9789027718150
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Non-commutative integration has its origin in the classical papers of Murray and von Neumann on rings of operators, and was introduced because of unsolved problems in unitary group representations and the elucidation of various aspects of quantum-mechanical formalism, together with formal calculus in such operator rings. These papers emphasized the interest in 1I -factors and pOinted out the remarkable behavior and 1 algebraic structure of the set of all unbounded closed operators a. ffiliated to such rings. The absence of power tools in functional analysis - mainly settled in their definitive form by A. Grothendieck around 1950-195- together with the pathological manipulation of algebraic operations on closed operators in Hilbert spaces, has limited ring-theory to the study of algebras of bounded operators with the main objective the difficult question of classifica tion up to isomorphisms of factors. This material has permitted a rigorous study of discrete systems in statistical mechanics but appears to be less convincing in other domains of physics (in the algebraic approach to field theory, for example). The striking role of Hamiltonians, Schrodinger operators and Lie group invariant properties in such areas of physics disappears in the so called C\*-approach. Codice articolo 9789027718150
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Unbounded Non-Commutative Integration (Mathematical Physics Studies, 7)
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Hardcover. Condizione: New. In shrink wrap. Looks like an interesting title! Codice articolo SL-9027718156
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