C*-algebras: Literature?

Question

I'd like to better understand states on C*-algebras.

What properties should I investigate and in which order?

(Positive functionals, extremal states, Schwarz's inequality, Kadison's inequality, what else?)

I suppose basic facts about functional analysis.

(C*-algebras, spectral theory, functional calculus, Banach-Alaoglu, etc.)

Thanks alot for your ideas!! :)

Answer 1

Just if somebody is interested...

I found the book by Zhu: An Introduction to Operator Algebras.

It just fits quite nicely when trying to get a first touch with the subject.

Answer 2

K. Davidson, "C*-Algebras by Example", Fields Institute Monographs, 1996.

Update. Added a more complete list. I am also studying C * algebras. A more complete list can be this.

O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics. 1", Texts and Monographs in Physics, Springer-Verlag, 1987.

K. R. Davidson, $C^*$-algebras by example", Fields Institute Monographs, Amer. Math.Soc., 1996.

J. Dixmier, $C^*$-Algebras", North Holland, 1982.

J. M. G. Fell and R. S. Doran, Representations of *-algebras, locally compact groups,and Banach *-algebraic bundles", Pure and Applied Mathematics vol. 125 and 126,Academic Press, 1988.

P. A. Fillmore, A user's guide to operator algebras", Canadian Mathematical Society Series of Monographs and Advanced Texts, Wiley Interscience, 1996.

R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras",Pure and Applied Mathematics vol. 100-II, Academic Press, 1986.

G. J. Murphy, $C*$-algebras and operator theory", Academic Press, 1990.

G. K. Pedersen, $C*$-algebras and their automorphism groups", Acad. Press, 1979.

V. S. Sunder, Functional analysis Spectral Theory", Birkhauser Verlag, 1998.

M. Takesaki, Theory of operator algebras I", Springer-Verlag, 1979.