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We construct a class of C~*-metric algebras. We prove that for a discrete group Γ with a 2-cocycle σ,the closure of the seminorm ||[M?, ·]|| on Cc(Γ, σ) is a Leibniz Lip-norm on the twisted reduced group C~*-algebra C*r(Γ, σ) for the pointwise multiplication operator M?on ?2(Γ), induced by a proper length function ? on Γ with the property of bounded θ-dilation. Moreover, the compact quantum metric space structures depend only on the cohomology class of 2-cocycles in the Lipschitz isometric sense. 相似文献
3.
Summary Let Γ=〈g
1〉*〈g
2〉*...*〈g
n
〉*... be a free product of cyclic groups with generators {g
i
}, andC
r
*
(Γ,℘
Λ) be the C*-algebra generated by the reduced group C*-algebraC
r
*
Γ and a set of projectionsP
gL associated with a subset Λ of {g
i
}. We prove the following: (1)C
r
*
(Γ,℘
Λ) is *-isomorphic to the reduced cross product
for certain Hausdorff compact spaceX
Λ constructed from Γ and its boundary ∂Γ. (2)C
r
*
(Γ,℘
Λ) is either a purely infinite, simple C*-algebra or an extension of a purely infinite, simple C*-altebra, depending on the
pair (Γ, Λ). (3)C
r
*
(Г,℘
Λ) is nuclear if and only if the subgroup ΓΛ generated by {g
i
}/Λ is amenable.
Partially supported by RMC grant 45/290/603 from the University of Newcastle
Partially supported by NSF grant DMS-9225076 and a Taft travel grant from the University of Cincinnati 相似文献
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Llolsten Kaonga 《Proceedings of the American Mathematical Society》2002,130(1):33-38
We give a sufficient condition for a unital C*-algebra to have no nontrivial projections, and we apply this result to known examples and to free products. We also show how questions of existence of projections relate to the norm-connectedness of certain sets of operators.
6.
Xin Li 《Mathematische Annalen》2010,348(4):859-898
We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a
result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples. Originally, our
motivation comes from algebraic number theory. 相似文献
7.
Farkhad Nematjonovich Arzikulov Shavkat Abdullayevich Ayupov 《Algebras and Representation Theory》2013,16(1):289-301
In the given article, enveloping C*-algebras of AJW-algebras are considered. Conditions are given, when the enveloping C*-algebra of an AJW-algebra is an AW*-algebra, and corresponding theorems are proved. In particular, we proved that if $\mathcal{A}$ is a real AW*-algebra, $\mathcal{A}_{sa}$ is the JC-algebra of all self-adjoint elements of $\mathcal{A}$ , $\mathcal{A}+i\mathcal{A}$ is an AW*-algebra and $\mathcal{A}\cap i\mathcal{A} = \{0\}$ then the enveloping C*-algebra $C^*(\mathcal{A}_{sa})$ of the JC-algebra $\mathcal{A}_{sa}$ is an AW*-algebra. Moreover, if $\mathcal{A}+i\mathcal{A}$ does not have nonzero direct summands of type I2, then $C^*(\mathcal{A}_{sa})$ coincides with the algebra $\mathcal{A}+i\mathcal{A}$ , i.e. $C^*(\mathcal{A}_{sa})= \mathcal{A}+i\mathcal{A}$ . 相似文献
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Raluca Dumitru Costel Peligrad 《Proceedings of the American Mathematical Society》2007,135(12):3977-3984
We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.
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We introduce noncommutative JB*-algebras which generalize both B*-algebras and JB*-algebras and set up the bases for a representation theory of noncommutative JB*-algebras. To this end we define noncommutative JB*-factors and study the factor representations of a noncommutative JB*-algebra. The particular case of alternative B*-factors is discussed in detail and a Gelfand-Naimark theorem for alternative B*-algebras is given. 相似文献
10.
We show that a C*-algebra is a 1-separably injective Banach space if and only if it is linearly isometric to the Banach space \({C_0(\Omega)}\) of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff space \({\Omega}\). 相似文献
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N. T. Nemesh 《Functional Analysis and Its Applications》2016,50(2):157-159
A criterion for the topological injectivity of an AW*-algebra as a right Banach module over itself is given. A necessary condition for a C* -algebra to be topologically injective is obtained. 相似文献
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We give an example of a non-trivial asymptotic representationof the reduced C*-algebra of a free group. This example allowsus to evaluate the asymptotic tensor C*-norm of some elementsin tensor product C*-algebras and to show semi-invertibilityof the non-invertible extension of C*r(2) considered by Haagerupand Thorbjørnsen. 相似文献
14.
Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe
such symmetries using crossed modules of groupoids. We define actions of crossed modules on C*-algebras and crossed products
for such actions, and justify these definitions with some basic general results and examples. 相似文献
15.
We describe the C*-algebras of the Heisenberg group H n , n??? 1, and the thread-like Lie groups G N , N??? 3, in terms of C*-algebras of operator fields. 相似文献
16.
Angel Rodríguez Palacios 《manuscripta mathematica》1988,61(3):297-314
A complex Banach spaceA which is also an associative algebra provided with a conjugate linear vector space involution * satisfying (a
2)*=(a
*)2, aa
*
a=a3 and ab+ba2ab for alla, b inA is shown to be a C*-algebra. The assumptions onA can be expressed in terms of the Jordan algebra obtained by symmetrization of the product ofA and are satisfied by any C*-algebra. Thus we obtain a purely Jordan characterization of C*-algebras. 相似文献
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Research supported by a grant from the Schweizerische Nationalfonds/Fonds national suisse 相似文献
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Silvia ScĂrlĂtescu-Murea 《Rendiconti del Circolo Matematico di Palermo》2000,49(3):561-574
This paper is concerned with the connection between the structure space of a locally C*-algebra and the set of its continuous
topologically irreducible *-representations. Properties of primitive ideals in such algebras are further investigated, for
instance, closed ideals are expressed as intersections of primitive ideals, by using that the Jacobson radical reduces to
0. 相似文献
20.
Let and be C*-dynamical systems and assume that is a separable simple C*-algebra and that α and β are *-automorphisms. Then the semicrossed products and are isometrically isomorphic if and only if the dynamical systems and are outer conjugate.
K. R. Davidson was partially supported by an NSERC grant. E. G. Katsoulis was partially supported by a summer grant from ECU 相似文献