Jean-Pierre Antoine, Atsushi Inoue, C. Trapani

Partial *- Algebras and Their Operator Realizations

• Broschiertes 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).

Produktdetails

• Mathematics and Its Applications 553
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-90-481-6176-8
• Softcover reprint of hardcover 1st ed. 2003
• Seitenzahl: 544
• Erscheinungstermin: 4. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 30mm
• Gewicht: 815g
• ISBN-13: 9789048161768
• ISBN-10: 9048161762
• Artikelnr.: 32008508

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.