共查询到19条相似文献,搜索用时 62 毫秒
1.
主要给出了迹稳定秩1的C*-代数的稳定有限性,证明了如果A是有单位元迹稳定秩1的C*-代数,则A是稳定有限的,引入了弱迹稳定秩1的定义,并且证明了如果有单位元的C*-代数A是迹稳定秩1的,则A是弱迹稳定秩1的.对于单的具有SP性质的有单位元的C*-代数A,如果A是弱迹稳定秩1的,则A是迹稳定秩1的.同时给出了迹稳定秩1的C*-代数的一个等价条件,证明了一个有单位元的可分的C*-代数A是迹稳定秩1的,等价于A=(t4)limn→∞(An,Pn),其中tsr(AN)=1. 相似文献
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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
3.
主要给出了迹稳定秩1的C~*-代数的稳定有限性,证明了如果A是有单位元迹稳定秩1的C~*-代数,则A是稳定有限的,引入了弱迹稳定秩1的定义,并且证明了如果有单位元的C~*-代数A是迹稳定秩1的,则A是弱迹稳定秩1的.对于单的具有SP性质的有单位元的C~*-代数A,如果A是弱迹稳定秩1的,则A是迹稳定秩1的.同时给出了迹稳定秩1的C~*-代数的一个等价条件,证明了一个有单位元的可分的C~*-代数A是迹稳定秩1的,等价于A=(t_4)limn→∞(A_n,p_n),其中tsr(A_n)=1. 相似文献
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给出了I(k)中迹极限C*-代数的某些性质.特别地给出了I(k)中迹极限c*-代数的的几个等价定义.利用此结果,证明了如果A是单的有单位元的C*-代数,并且A具有唯一的标准迹,A=(t4)Lim n→∞ (An,pn),其中An∈I(k),则A=(t4) lim n→∞(An,pn),其中An∈I(O).最后给出了I(k)中迹极限C*-代数的Ko-群的消去律性质. 相似文献
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设0→B(j)→E(π)→A→0是有单位元C*-代数E的一个扩张,其中A是有单位元纯无限单的C*-代数,B是E的闭理想.当B是E的本性理想并且同时是单的、可分的而且具有实秩零及性质(PC)时,证明了Ko(E)={[p]| p是E\B中的投影};当B是稳定C*-代数时,证明了对任意紧的Hausdorff空间X,有(u)(C(X,E))/(u)o(C(X,E))≌K1(C(X,E)). 相似文献
8.
设0→B■E■A→0是有单位元C~*-代数E的一个扩张,其中A是有单位元纯无限单的C~*-代数,B是E的闭理想.当B是E的本性理想并且同时是单的、可分的而且具有实秩零及性质(PC)时,证明了K_0(E)={[p]| p是E\B中的投影};当B是稳定C~*-代数时,证明了对任意紧的Hausdorff空间X,有■(C(X,E))/■_0(C(X,E))≌K_1(C(X,E)). 相似文献
9.
引入C~*-代数迹迹秩的概念,讨论它的基本性质.另外,迹迹秩为零和迹拓扑秩为零的C~*-代数等价,同时讨论这类代数的拟对角扩张性质.设O→I→A→A/I→O是拟对角扩张的短正合列,证明如果TTR(I)≤k且TTR(A/I)=0,则TTR(A)≤k. 相似文献
10.
侯成军 《数学年刊A辑(中文版)》2003,(2)
本文证明由拓扑混合的Smale空间上的渐进等价关系定义的广群C*-代数及其相应的Ruelle代数有唯一的迹态;在拓扑可迁的情形下,证明此C*-代数的迹态构成了一个单形,此单形顶点的个数等于“Smale谱分解”中基本空间的个数,单形的重心是该C*-代数的唯一的αa-不变迹态;此回答了I.Putnam的一个猜测. 相似文献
11.
Takashi Sakamoto 《Proceedings of the American Mathematical Society》1999,127(1):205-210
For a non-unital C-algebra , let be the C-algebra obtained from by adjoining an identity. In this paper we show that
where is a locally compact Hausdorff space with .
12.
Let A?(??) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that A?(??) has Bass and topological stable ranks equal to 2, which settles the conjecture made by Brett Wick in [18]. We also give a necessary and sufficient condition for reducibility in some real algebras of functions on symmetric domains with holes, which is a generalization of the main theorem in [18]. A sufficient topological condition on the symmetric open set ?? is given for the corresponding real algebra A?(??) to have Bass stable rank equal to 1 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Rami Grossberg Alexei Kolesnikov Ivan Tomai Monica Van Dieren 《Mathematical Logic Quarterly》2003,49(2):115-128
The new result of this paper is that for θ( x ; a )‐stable (a weakening of “T is stable”) we have S1[θ( x ; a )] = D[θ( x ; a ), L, ∞]. S1 is Hrushovski's rank. This is an improvement of a result of Kim and Pillay, who for simple theories under the (strong) assumption that either of the ranks be finite obtained the same identity. Only the first equality is new, the second equality is a result of Shelah from the seventies. We derive it by studying localizations of several rank functions, we get the following Main Theorem. Suppose that μ is regular satisfying μ ≥ |T|+, p is a finite type, and Δ is a set of formulas closed under Boolean operations. If either (a) R[p, Δ, μ+] < ∞ or (b) p is Δ‐stable and μ satisfies “for every sequence {μi : i < |Δ| + ?0} of cardinals μi < μ we have that holds”, then S[p, Δ, μ+] = D[p, Δ, μ+] = R[p, Δ, μ+]. The S rank above is a localized version of Hrushovski's S1 rank. This rank, as well as our systematic use of local stability, allows us to get a more conceptual proof of the equality of D and R, which is an old result of Shelah. A particular (asymptotic) case of the theorem offers a new sufficient condition for the equality of S1 and D[·, L, ∞]. We also manage, due to a more general approach, to avoid some combinatorial difficulties present in Shelah's original exposition. 相似文献
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Raymond Mortini 《代数通讯》2017,45(3):1260-1269
In the context of commutative C*-algebras, we solve a problem related to a question of M. Rieffel by showing that the all-units rank and the norm-one rank coincide with the topological stable rank. We also introduce the notion of unitary M-stable rank for an arbitrary commutative unital ring and compare it with the Bass stable rank. In case of uniform algebras, a su?cient condition for norm-one reducibility is given. 相似文献
15.
Bruce Blackadar 《Proceedings of the American Mathematical Society》2004,132(10):2945-2950
We give a treatment of Rieffel's theory of stable rank for C*-algebras in terms of left invertibility of generalized nonsquare matrices, and prove that if is a full projection in a unital C*-algebra , then the stable rank of the corner is at least as large as the stable rank of .
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Let A and B be C*-algebras. An extension of B by A is a short exact sequence 0 →A -→E→B→0. (*) Suppose that A is an AT-algebra with real rank zero and B is any .AT-algebra. We prove that E is an AT-algebra if and only if the extension (*) is quasidiagonal. 相似文献
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We characterize the values of the stable rank for Leavitt path algebras by giving concrete criteria in terms of properties of the underlying graph.
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In this paper, we give a class of C*-algebras with non-stable K
1-group property which include the example non-simple tracial topological rank zero and stable rank two C*-algebra given by Lin and Osaka. 相似文献
19.
We show that if is the uniform algebra of almost periodic functions, then the set cannot be dense in for any positive integer .