Titlebook: Partial *- Algebras and Their Operator Realizations; Jean-Pierre Antoine,Atsushi Inoue,Camillo Trapani Book 2002 Springer Science+Business

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Tomita—Takesaki Theory in Partial O*-Algebraszed vectors for a partial GW*-algebra. Section 5.6 deals with some particular cases of standard or modular generalized vectors for partial O*-algebras (generalized vectors associated to individual vectors (Section 5.6.1);

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*-Representations of Partial *-AlgebrasSqabaaaaa!42DC!]]

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Book 2002bounded 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.*.-alg

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Physical Applicationsis a detailed study of automorphisms and derivations of partial *-algebras. Then we consider some applications of quasi *-algebras to local (or quasi-local) quantum theories, such as quantum field theory (Wightman fields) or Quantum Statistical Mechanics (spin systems, Bose gases).

Anecdote

Partial *-Algebras*-algebras (Section 6.2.2), and CQ *-algebras (Section 6.2.3). We also describe in detail a series of concrete examples, which are of two types, partial *-algebras of functions (Section 6.3.1) or partial *-algebras of operators on lattices of Hilbert spaces (Section 6.3.2). Representation theory will be covered in the subsequent chapters.