Nuclear C*-algebra

In mathematics, a nuclear C*-algebra is a C*-algebra A such that the injective and projective C*-cross norms on AB are the same for every C*-algebra B. This property was first studied by Takesaki (1964) under the name "Property T", which is not related to Kazhdan's property T.

CharacterizationsEdit

Nuclearity admits the following equivalent characterizations:

See alsoEdit

ReferencesEdit

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  • Takesaki, Masamichi (1964), "On the cross-norm of the direct product of C*-algebras", The Tohoku Mathematical Journal, Second Series, 16: 111–122, doi:10.2748/tmj/1178243737, ISSN 0040-8735, MR 0165384
  • Takesaki, Masamichi (2003), "Nuclear C*-algebras", Theory of operator algebras. III, Encyclopaedia of Mathematical Sciences, 127, Berlin, New York: Springer-Verlag, pp. 153–204, ISBN 978-3-540-42913-5, MR 1943007