Partial *- Algebras and Their Operator Realizations (Mathematics and Its Applications (closed)): 553 - Brossura

Antoine, J-P.

 
9789048161768: Partial *- Algebras and Their Operator Realizations (Mathematics and Its Applications (closed)): 553
Brossura
ISBN 10: 9048161762 ISBN 13: 9789048161768
Casa editrice: Springer, 2010

Sinossi

Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. Schmüdgen [1990] and A. Inoue [1998]). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on this topic.
The first part is devoted to partial O*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics.
The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).

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Contenuti

Foreword. Introduction. I: Theory of Partial O*-Algebras. 1. Unbounded Linear Operators in Hilbert Spaces. 2. Partial O*-Algebras. 3.Commutative Partial O*-Algebras. 4. Topologies on Partial O*-Algebras. 5. Tomita Takesaki Theory in Partial O*-Algebras. II: Theory of Partial *-Algebras. 6. Partial *-Algebras. 7. *-Representations of Partial *-Algebras. 8. Well-behaved X>*-Representations. 9. Biweights on Partial *-Algebras. 10. Quasi *-Algebras of Operators in Rigged Hilbert Spaces. 11. Physical Applications. Outcome. Bibliography. Index.

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Editore
Springer
Data di pubblicazione
2010
Lingua
Inglese
ISBN 10 
9048161762
ISBN 13 
9789048161768
Rilegatura
Copertina flessibile
Numero di pagine
544
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
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Hamburg
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Altre edizioni note dello stesso titolo

9781402010255: Partial-Algebras and Their Operator Realizations: 553

Edizione in evidenza

ISBN 10:  1402010257 ISBN 13:  9781402010255
Casa editrice: Kluwer Academic Pub, 2002
Rilegato