Jean-Pierre Antoine, Atsushi Inoue, C. Trapani

Partial *- Algebras and Their Operator Realizations

• Gebundenes Buch

Produktbeschreibung

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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Produktdetails

• Mathematics and Its Applications 553
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-1-4020-1025-5
• 2003
• Seitenzahl: 546
• Erscheinungstermin: 31. Dezember 2002
• Englisch
• Abmessung: 241mm x 160mm x 35mm
• Gewicht: 976g
• ISBN-13: 9781402010255
• ISBN-10: 1402010257
• Artikelnr.: 22389517

Inhaltsangabe

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 *-Representations.- 9 Biweights on Partial *-Algebras.- 10 Quasi *-Algebras of Operators in Rigged Hilbert Spaces.- 11 Physical Applications.- Outcome.