Abstract
In Part I, we have thoroughly analyzed the most important partial *-algebras of operators, namely partial O*-algebras, with the aim of generalizing some crucial elements of the theory of C*-algebras and von Neumann algebras. In Part II, we return to abstract partial *-algebras and set up their representation theory, which most of the time will give rise to partial O*-algebras. The present chapter is devoted to the general aspects of the abstract theory of partial *-algebras and the analysis of several particular classes, namely locally convex partial *-algebras (Section 6.1.2), Banach partial *-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.
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Antoine, JP., Inoue, A., Trapani, C. (2002). Partial *-Algebras. In: Partial *-Algebras and Their Operator Realizations. Mathematics and Its Applications, vol 553. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0065-8_6
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DOI: https://doi.org/10.1007/978-94-017-0065-8_6
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