Partial *- Algebras and Their Operator Realizations

di J-P Antoine (Autore)

I. Inoue (Autore)

C. Trapani (Autore)

Springer, 2010

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).

• Autore: J-P Antoine, I. Inoue, C. Trapani
• Editore: Springer
• Collana: Mathematics and Its Applications
• Anno: 2010
• Rilegatura: Paperback / softback
• Pagine: 522 p.
• Dimensioni: 235 x 155 mm
• EAN: 9789048161768

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