I am trying to get a better understanding of "real" $C^*$-algebras. I encountered them in the paper

D. Voiculescu, Dual algebraic structures, J. Operator Theory 17(1987), 85-98,

which cites

G.G. Kasparov, Hilbert $C^*$-modules: theorems of Stinespring and Voiculescu, J. Operator Theory, 4(1980), 133-150.

Roughly speaking, these "real" $C^*$-algebras are complexifications of real $C^*$-algebras. They are defined as complex $C^*$-algebras equipped with an additional antilinear multiplicative involution.

I would be grateful for any pointers to additional literature on these algebras. (The quotation marks and the star in their name make it more tricky to find them with google...).


Real operator algebras, Bing-Ren Li, Pub. Co. Pte. Ltd, 2003 (and the bibliography in that book). Also the other operator algebra book by the same author has parts about real operator algebras (together with the traditional complex ones)

An older book is by Goodearl, and a classical paper is http://jlms.oxfordjournals.org/content/s2-47/1/97.full.pdf (and references in it).

You can also seacr for papers citing them: example1, example2


There is a book by Herbert Schröder called "K-Theory for Real C*-algebras and Applications", which can be found on mathscinet and has a Google Books entry (sadly without preview).

  • 1
    $\begingroup$ Thank you for this reference, I am sorry that I can't accept both answers. $\endgroup$ – UwF Apr 11 '14 at 19:53

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