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Titlebook: An Introduction to C*-Algebras and the Classification Program; Karen R. Strung,Francesc Perera Textbook 2021 The Editor(s) (if applicable)

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Nachuntersuchung und ManualbefundePositive elements play a very important role in the theory of C*-algebras. They allow us to define a partial order on the self-adjoint elements which is a key part of the structure of any C*-algebra.
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Nachuntersuchung und ManualbefundeIn this section we will see that every abstract C*-algebra is *-isomorphic to a self-adjoint closed subalgebra of B(H), for some Hilbert space H. That is to say, the class of abstract C*-algebras and the class of concrete C*-algebras coincide.
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Nachuntersuchung und ManualbefundeWe have seen that C*-algebras boast a number of good structural properties that distinguish them from arbitrary Banach algebras. There are various types of maps one could consider between C*-algebras which aim at preserving particular C*-algebraic properties.
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