“Nuclear C*-algebra”的意思、由来-开放百科全书

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Nuclear C*-algebra

释义

Characterizations
See also
References

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

Characterizations

Nuclearity admits the following equivalent characterizations:

The identity map, as a completely positive map, approximately factors through matrix algebras. By this equivalence, nuclearity can be considered a noncommutative analogue of the existence of partitions of unity.
The enveloping von Neumann algebra is injective.
It is amenable as a Banach algebra.
It is isomorphic to a C-subalgebra B of the Cuntz algebra with the property that there exists a conditional expectation from to B. This condition is only equivalent to the others for separable C-algebras.

References

{{Citation | last1=Connes | first1=Alain | author1-link=Alain Connes | title=Classification of injective factors. | jstor=1971057 | mr=0454659 | year=1976 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=104 | issue=1 | pages=73–115 | doi=10.2307/1971057}}
{{Citation | last1=Effros | first1=Edward G. | last2=Ruan | first2=Zhong-Jin | title=Operator spaces | url=http://www.oup.com/us/catalog/general/subject/Mathematics/PureMathematics/?ci=9780198534822 | publisher=The Clarendon Press Oxford University Press | series=London Mathematical Society Monographs. New Series | isbn=978-0-19-853482-2 | mr=1793753 | year=2000 | volume=23}}
{{Citation | last1=Lance | first1=E. Christopher | title=Operator algebras and applications, Part I (Kingston, Ont., 1980) | publisher=Amer. Math. Soc. | location=Providence, R.I. | series=Proc. Sympos. Pure Math. | mr=679721 | year=1982 | volume=38 | chapter=Tensor products and nuclear C-algebras | pages=379–399}}
{{Citation | last1=Pisier | first1=Gilles | title=Introduction to operator space theory | publisher=Cambridge University Press | series=London Mathematical Society Lecture Note Series | isbn=978-0-521-81165-1 | mr=2006539 | year=2003 | volume=294}}
{{Citation | last1=Rørdam | first1=M. | title=Classification of nuclear C-algebras. Entropy in operator algebras | publisher=Springer-Verlag | location=Berlin, New York | series=Encyclopaedia Math. Sci. | mr=1878882 | year=2002 | volume=126 | chapter=Classification of nuclear simple C-algebras | pages=1–145}}
{{Citation | last1=Takesaki | first1=Masamichi | title=On the cross-norm of the direct product of C-algebras | mr=0165384 | year=1964 | journal=The Tohoku Mathematical Journal. Second Series | issn=0040-8735 | volume=16 | pages=111–122 | doi=10.2748/tmj/1178243737}}
{{Citation | last1=Takesaki | first1=Masamichi | title=Theory of operator algebras. III | publisher=Springer-Verlag | location=Berlin, New York | series=Encyclopaedia of Mathematical Sciences | isbn=978-3-540-42913-5 | mr=1943007 | year=2003 | volume=127 | chapter=Nuclear C-algebras | pages=153–204}}

{{DEFAULTSORT:Nuclear C-algebra}}C*-algebra#C*-algebra nucleare

1 : C*-algebras

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Characterizations

See also

References