By Lin H.
The idea and functions of C*-algebras are on the topic of fields starting from operator conception, crew representations and quantum mechanics, to non-commutative geometry and dynamical platforms. by means of Gelfand transformation, the idea of C*-algebras can be considered as non-commutative topology. a couple of decade in the past, George A. Elliott initiated this system of category of C*-algebras (up to isomorphism) by means of their K-theoretical info. It began with the category of AT-algebras with genuine rank 0. because then nice efforts were made to categorise amenable C*-algebras, a category of C*-algebras that arises so much evidently. for instance, a wide classification of straightforward amenable C*-algebras is came upon to be classifiable. the appliance of those effects to dynamical structures has been verified. This ebook introduces the hot improvement of the speculation of the class of amenable C*-algebras - the 1st such try out. the 1st 3 chapters current the fundamentals of the idea of C*-algebras that are quite vital to the idea of the type of amenable C*-algebras. bankruptcy four deals the category of the so-called AT-algebras of actual rank 0. the 1st 4 chapters are self-contained, and will function a textual content for a graduate direction on C*-algebras. The final chapters comprise extra complex fabric. specifically, they take care of the category theorem for easy AH-algebras with actual rank 0, the paintings of Elliott and Gong. The publication comprises many new proofs and a few unique effects with regards to the type of amenable C*-algebras. in addition to offering an advent to the idea of the type of amenable C*-algebras, it's a accomplished reference for these extra accustomed to the topic.
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