Abstract
We initiate a general study of ultraproducts of C*-algebras, including topics on representations, homomorphisms, isomorphisms, positive linear maps and their ultraproducts. We partially settle a question of D. McDuff by proving, for a finite von Neumann algebra with a separable predual, that the continuum hypothesis implies the isomorphism of all of its tracial ultrapowers with respect to different free ultrafilters on the natural numbers. The analog for C*-ultrapowers of separable C*-algebras is equivalent to the continuum hypothesis. We also prove a finite local reflexivity theorem for operator spaces that implies that the second dual of a C*-algebra can be embedded in some ultra-power of the algebra using a completely positive completely isometric map.
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© 2001 Springer Basel AG
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Ge, L., Hadwin, D. (2001). Ultraproducts of C*-algebras. In: Kérchy, L., Gohberg, I., Foias, C.I., Langer, H. (eds) Recent Advances in Operator Theory and Related Topics. Operator Theory: Advances and Applications, vol 127. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8374-0_17
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DOI: https://doi.org/10.1007/978-3-0348-8374-0_17
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9539-2
Online ISBN: 978-3-0348-8374-0
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