Unbounded non-commutative integration
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Bibliographic Information
Unbounded non-commutative integration
（Mathematical physics studies, v. 7）
D. Reidel Pub. Co. , Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, c1985
Available at / 27 libraries
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University of Tsukuba Library, Library on Library and Information Science
421.5:Ma-72:7931003830
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc19:530.15/j9792021266908
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Note
Bibliography: p. 189-190
Includes index
Description and Table of Contents
Description
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.
Table of Contents
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.
by "Nielsen BookData"
