共查询到20条相似文献,搜索用时 15 毫秒
1.
Order unit property of a positive element in aC* -algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary
C*-subalgebras of aC* -algebra are characterized. 相似文献
2.
In this paper, we study the problem of when the corona algebra of a non-unital C*-algebra is purely infinite. A complete answer
is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result
relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the
algebra, and to the behaviour of corona projections, despite the fact that there is no real rank zero condition. 相似文献
3.
The authors prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banach modules over a unital C*-algebra, and prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banach modules over a unital Banach algebra. 相似文献
4.
We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C~*-algebra. We also show that if a unital C~*-algebra can be approximately embedded into some tensorially self absorbing C~*-algebra C(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the Cuntz algebra O_2),then we can construct a simple separable unital generalized inductive limit. When C is simple and infinite(resp.properly infinite), the construction is also infinite(resp. properly infinite). When C is simple and approximately divisible, the construction is also approximately divisible. When C is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero. 相似文献
5.
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.
MA Xiujuan School of Sciences Hebei University of Technology Tianjin China Mathematics Institute Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2005,48(8):1144-1151
Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra. 相似文献
7.
Lajos Molnár 《Archiv der Mathematik》2014,102(1):83-89
In this note we show that the bilocal *-automorphisms of the C*-algebra B(H) of all bounded linear operators acting on a complex infinite dimensional separable Hilbert space H are precisely the unital algebra *-endomorphisms of B(H). 相似文献
8.
本文引入了一类迹稳定秩一的C*-代数,证明了迹稳定秩一的C*-代数与AF-代数的张量积是迹稳定秩一的,得到了一个可分的单的有单位元的迹稳定秩一的,并且具有SP性质的C*-代数是稳定秩一的.同时,还讨论了迹稳定秩一的C*-代数的K-群的某些性质. 相似文献
9.
We show that every unital linear bijection which preserves the maximal left ideals from a semi-simple Banach algebra onto a C-algebra of real rank zero is a Jordan isomorphism. Furthermore, every unital self-adjoint linear bijection on a countably decomposable factor von Neumann algebra is maximal left ideal preserving if and only if it is a *-automorphism.
10.
π-complemented algebras are defined as those algebras (not necessarily associative or unital) such that each annihilator ideal is complemented by other annihilator ideal. Let A be a semiprime algebra. We prove that A is π-complemented if, and only if, every idempotent in the extended centroid of A lies in the centroid of A. We also show the existence of a smallest π-complemented subalgebra of the central closure of A containing A. In the case that A is a C*-algebra, this subalgebra turns out to be a norm dense *-subalgebra of the bounded central closure of A. It follows that a C*-algebra is boundedly centrally closed if, and only if, it is π-complemented. 相似文献
11.
We construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the Fell bundle. We study when the reduced C*-algebra for an inverse semigroup action on a groupoid by partial equivalences coincides with the reduced groupoid C*-algebra of the transformation groupoid, giving both positive results and counterexamples. 相似文献
12.
13.
There are many different crossed products by an endomorphism of a C*-algebra, and constructions by Exel and Stacey have proved particularly useful. Here we consider Exel crossed products associated
to transfer operators which extend to be unital on the multiplier algebra. We show that every Exel crossed product is isomorphic
to a Stacey crossed product, though by a different endomorphism of a different C*-algebra. We apply this result to a variety of Exel systems, including those associated to shifts on the path spaces of directed
graphs. 相似文献
14.
HUANG XuJian 《中国科学 数学(英文版)》2011,(6)
The main theme of this paper is to consider a notion of 'approximately unital operator systems' including both C*-algebras and unital operator systems.The goals are to prove a version of the Choi-Effros theorem for these systems,to introduce a functorial process for forming an approximately unital operator systems from a given matrix ordered vector space with a proper approximate order unit,to study second duals of these objects and to prove that a C*-algebra can be characterized as an approximately unital ... 相似文献
15.
Lawrence A. Harris Richard V. Kadison 《Proceedings of the American Mathematical Society》1996,124(8):2415-2422
The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.
16.
The authors prove that the crossed product of an infinite dimensional simple separable unital C*-algebra with stable rank one by an action of a finite group with the tracial Rokhlin property has again stable rank one. It is also proved that the crossed product of an infinite dimensional simple separable unital C*-algebra with real rank zero by an action of a finite group with the tracial Rokhlin property has again real rank zero. 相似文献
17.
Osamu Hatori Takeshi Miura Hiroyuki Takagi 《Journal of Mathematical Analysis and Applications》2007,326(1):281-296
Let T be a surjective map from a unital semi-simple commutative Banach algebra A onto a unital commutative Banach algebra B. Suppose that T preserves the unit element and the spectrum σ(fg) of the product of any two elements f and g in A coincides with the spectrum σ(TfTg). Then B is semi-simple and T is an isomorphism. The condition that T is surjective is essential: An example of a non-linear and non-multiplicative unital map from a commutative C*-algebra into itself such that σ(TfTg)=σ(fg) holds for every f,g are given. We also show an example of a surjective unital map from a commutative C*-algebra onto itself which is neither linear nor multiplicative such that σ(TfTg)⊂σ(fg) holds for every f,g. 相似文献
18.
We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of unitary equivalence of automorphisms of a separable unital C*-algebra: Such relation is either smooth or not even classifiable by countable structures. 相似文献
19.
本文描述了AF C*-代数中闭Lie理想,证明了如果AF C*-代数A中的线性流形L 是A的闭Lie理想,则存在A的闭结合理想I和A的典型masa D中的闭子代数EI使得[A,I](?)L(?)I EI,并且A中每一个这种形式的闭子空间都是A的闭Lie理想. 相似文献
20.
We realize Kellendonk’s C*-algebra of an aperiodic tiling as the tight C*-algebra of the inverse semigroup associated to the
tiling, thus providing further evidence that the tight C*-algebra is a good candidate to be the natural associative algebra
to go along with an inverse semigroup. 相似文献