共查询到20条相似文献，搜索用时 15 毫秒
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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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In this article, we show that a group is abelian if and only if every two elements of the same order commute. 相似文献
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This note is concerned with generalizations of commutativity. We introduce identity-symmetric and right near-commutative, and study basic structures of rings with such ring properties. It is shown that if R is an identity-symmetric ring, then the set of all nilpotent elements forms a commutative subring of R. Moreover, identity-symmetric regular rings are proved to be commutative. The near-commutativity is shown to be not left-right symmetric, and we study some conditions under which the near-commutativity is left-right symmetric. We also examine the near-commutativity of skew-trivial extensions, which has a role in this note. 相似文献
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Witold Majdak Zoltá n Sebestyé n Jan Stochel James E. Thomson 《Proceedings of the American Mathematical Society》2006,134(6):1687-1699
Criteria for the existence of lifts of operators intertwining subnormal operators are established. The main result of the paper reduces lifting questions for general subnormal operators to questions about lifts of cyclic subnormal operators. It is shown that in general the existence of local lifts (i.e. those coming from cyclic parts) for a pair of subnormal operators does not imply the existence of a global lift. However this is the case when minimal normal extensions of subnormal operators in question are star-cyclic.
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ＣＥＲＴＡＩＮＣＯＭＭＵＴＡＴＩＶＩＴＹＣＯＮＤＩＴＩＯＮＳＦＯＲＲＩＮＧＳＷＩＴＨＵＮＩＴＹＶ．Ｗ．Ｊａｃｏｂ，Ｍ．ＡｓｈｒａｆａｎｄＭ．Ａ．Ｑｕａｄｒｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＡｌｉｇａｒｈＭｕｓｌｉｍＵｎｉｖｅｒｓｉｔ... 相似文献
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We give three kinds of characterizations of the commutativity of C- algebras. The first is the one from operator monotone property of functions regarded as the nonlinear version of Stinespring theorem, the second one is the characterization of commutativity of local type from expansion formulae of related functions and the third one is of global type from multiple positivity of those nonlinear positive maps induced from functions.
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Daisuke Kishimoto 《Topology and its Applications》2010,157(12):1949-1954
It is a classical result by Bott that SU(s) and SU(t) homotopy commute in SU(n) if and only if s+t?n. We consider the p-localization analog of this problem and give an answer at odd primes. 相似文献
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We give an explicit formula for a right inverse of the trace operator from the Sobolev space H1(T) on a triangle T to the trace space H1/2(?T) on the boundary. The lifting preserves polynomials in the sense that if the boundary data are piecewise polynomial of degree N, then the lifting is a polynomial of total degree at most N and the lifting is shown to be uniformly stable independently of the polynomial order. Moreover, the same operator is shown to provide a uniformly stable lifting from L2(?T) to H1/2(T). Finally, the lifting is used to construct a uniformly bounded right inverse for the normal trace operator from the space H (div; T) to H–1/2(?T) which also preserves polynomials. Applications to the analysis of high order numerical methods for partial differential equations are indicated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Extending the notion of probability to the automorphisms of a group, we find the probability of an arbitrarily chosen automorphism of a group fixing an arbitrary element of the group. 相似文献
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A. E. Litvak V. D. Milman A. Pajor N. Tomczak-Jaegermann 《Functional Analysis and Its Applications》2006,40(4):298-303
We prove an “entropy extension-lifting theorem.” It consists of two inequalities for the covering numbers of two symmetric convex bodies. The first inequality, which can be called an “entropy extension theorem,” provides estimates in terms of entropy of sections and should be compared with the extension property of ?∞. The second one, which can be called an “entropy lifting theorem,” provides estimates in terms of entropies of projections. 相似文献
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In the current article, we prove the crossed product C*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C*-algebra is strongly quasidiagonal again. We also show that a just-infinite C*-algebra is quasidiagonal if and only if it is inner quasidiagonal. Finally, we compute the topological free entropy dimension in just-infinite C*-algebras. 相似文献
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殷先军 《数学的实践与认识》2006,36(3):240-243
设{s1∨s2,y0}为具有公共切点y0的两个圆s1、s2的并集,通过对s1∨s2中的每一个闭路径定义一个“点列”,给出基本群π1(s1∨s2,y0)非交换性的一个新的证明. 相似文献
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黄益生 《纯粹数学与应用数学》1999,15(3):27-32,17
得到交换 Ｂ Ｃ Ｉ代数 Ｘ 的一些进一步性质．主要结果有：（ｉ） 给出 Ｘ 的交换性的两个特征;（ｉｉ） 证明对任意 ｃ∈ Ｘ,ｃ 的初始段 Ａ（ｃ）关于 Ｂ Ｃ Ｉ序≤构成一个分配格（ Ａ（ｃ）;≤）;（ｉｉｉ） 指出 Ｘ 未必是拟交换的 相似文献
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Ricardo N. Oliveira Said N. Sidki 《Bulletin of the Brazilian Mathematical Society》2009,40(2):149-180
The second author introduced notions of weak permutablity and commutativity between groups and proved the finiteness of a
group generated by two weakly permutable finite subgroups. Two groups H, K weakly commute provided there exists a bijection f: H → K which fixes the identity and such that h commutes with its image h
f
for all h ∈ H. The present paper gives support to conjectures about the nilpotency of groups generated by two weakly commuting finite abelian
groups H, K.
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