共查询到19条相似文献,搜索用时 109 毫秒
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The N-Isometric Isomorphisms in Linear N-Normed C^*-Algebras 总被引:3,自引:3,他引:0
Chun-Gil PARK Themistocles M. RASSIAS 《数学学报(英文版)》2006,22(6):1863-1890
We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^*-algebra. The main purpose of this paper is to investigate N-isometric C^*-algebra isomorphisms between linear N-normed C^*-algebras, N-isometric Poisson C^*-algebra isomorphisms between linear N-normed Poisson C^*-algebras, N-isometric Lie C^*-algebra isomorphisms between linear N-normed Lie C^*-algebras, N-isometric Poisson JC^*-algebra isomorphisms between linear N-normed Poisson JC^*-algebras, and N-isometric Lie JC^*-algebra isomorphisms between linear N-normed Lie JC^*-algebras.
Moreover, we prove the Hyers- Ulam stability of t:heir N-isometric homomorphisms. 相似文献
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Ming LIU Li Ning JIANG Guo Sheng ZHANG 《数学学报(英文版)》2007,23(6):1121-1128
This paper defines a pairing of two finite Hopf C^*-algebras A and B, and investigates the interactions between them. If the pairing is non-degenerate, then the quantum double construction is given. This construction yields a new finite Hopf C^*-algebra D(A, B). The canonical embedding maps of A and B into the double are both isometric. 相似文献
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Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f : X →Y satisfies the functional equation 2d f(∑^2d j=1(-1)^j+1xj/2d)=∑^2dj=1(-1)^j+1f(xj) with f(0) = 0 if and only if the mapping f : X→ Y is Cauchy additive, and prove the stability of the functional equation (≠) in Banach modules over a unital C^*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C^*-algebras, Poisson C^*-algebras or Poisson JC^*- algebras. As an application, the authors show that every almost homomorphism h : A →B of A into is a homomorphism when h((2d-1)^nuy) =- h((2d-1)^nu)h(y) or h((2d-1)^nuoy) = h((2d-1)^nu)oh(y) for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^*-algebras, Poisson C^*-algebras or Poisson JC^*-algebras. 相似文献
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Given two nuclear C^*-algebras A1 and A2 with states φ1 and φ2, we show that the monotone product C^*-algebra A1 △→ A2 is still nuclear. Furthermore, if both the states φ1 and φ2 are faithful, then the monotone product ,A1 △→ A2 is nuclear if and only if the C^*-algebras ,A1 and A2 both are nuclear. 相似文献
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Wen Ming WU Li Guang WANG 《数学学报(英文版)》2007,23(3):491-496
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Given a C^*-algebra A and a comultiplication Ф on A, we show that the pair (A, Ф) is a compact quantum group if and only if the associated multiplier Hopf ^*-algebra (A, ФA) is a compact Hopf ^*-algebra. 相似文献
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探讨了C^n中单位球面S上Berezin变换和Toeplitz算子的性质,证明了由{Tφ,φ∈L^∞ (S)}所生成的C^*-代数中算子T的符号恰好为单位球B上函数T(称为T的Berezin变换)的非切向边界值.此外,本文还得到了经典Toeplitz符号演算的有趣推广. 相似文献
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Wei Wu 《数学学报(英文版)》2008,24(7):1139-1154
The author generalizes the Arzela-Ascoli theorem to the setting of matrix order unit spaces, extending the work of Antonescu-Christensen on unital C^*-algebras. This gives an affirmative answer to a question of Antonescu and Christensen. 相似文献
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设G为一个离散群,(G,G_ )为一个拟偏序群使得G_ ~0=G_ ∩G_ ~(-1)为G的非平凡子群。令[G]为G关于G_ ~0的左倍集全体,|G_ |为[G]的正部。记T~(G_ )和T~([G_ ])为相应的Toeplitz代数。当存在一个从G到G_ ~0上的形变收缩映照时,我们证明了T~(G_ )酉同构于T~([G_ ])×C_r~*(G_ ~0)的一个C_-~*c子代数。若进一步,G_ ~0还为G的一个正规子群,则T~(G_ )与T~([G_ ])×C_r~*(G_ ~0)酉同构。 相似文献
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Valdis Laan 《Semigroup Forum》2005,70(2):188-207
Considering the wreath product functor $G wr H:{\cal A} wr^G{\cal B} \rightarrow \SET$ of functors $G: {\cal A}\rightarrow \SET$ and
$H: {\cal B}\rightarrow \SET$ over small categories $ {\cal A}$ and $ {\cal B}$, we prove that if tensor multiplication by the functor $G\wrr H$ preserves $ {\cal D}$-limits, where ${\cal D}$ is a small category, then tensor multiplication by $G$ preserves ${\cal D}$-limits, and if tensor multiplication by the functor $G wr H$ preserves ${\cal D}$-limits of representables then tensor multiplications by $G$ and $H$ preserve $ {\cal D}$-limits of representables. We also study flatness and pullback flatness of the wreath product of set-valued functors. 相似文献
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本文利用差方法对自反MD设计SCMD$(4mp, p,1)$的存在性给出了构造性证明, 这里$p$为奇素数, $m$为正整数. 相似文献
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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
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Let =(A C X B)be a 2×2 operator matrix acting on the Hilbert space н( )κ.For given A ∈B (H),B ∈B(K)and C ∈B(K,H)the set Ux∈B(H,к)σe(Mx)is determined,where σe(T)denotes the essential spectrum. 相似文献
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The authors obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation:αu/αt=△u-b(x,t)u~σ on complete noncompact manifolds with Ricci curvature bounded from below,where 0σ1 is a real constant,and b(x,t) is a function which is C~2 in the x-variable and C~1 in the t-variable. 相似文献
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An LRHTS(v)(or LARHTS(v)) is a collection of {(X, B i) : 1 ≤ i ≤ 4(v-2)},where X is a v-set, each(X, B i) is a resolvable(or almost resolvable) HTS(v), and all B i s form a partition of all cycle triples and transitive triples on X. An OLRHTS(v)(or OLARHTS(v))is a collection {(Y \{y}, A j y) : y ∈ Y, j = 0, 1, 2, 3}, where Y is a(v + 1)-set, each(Y \{y}, A j y)is a resolvable(or almost resolvable) HTS(v), and all A j y s form a partition of all cycle and transitive triples on Y. In this paper, we establish some directed and recursive constructions for LRHTS(v), LARHTS(v), OLRHTS(v), OLARHTS(v) and give some new results. 相似文献
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Problems on product of formations 总被引:1,自引:0,他引:1
In formation theory, one of the interesting problems is the existence of a saturated formation which is a product of non-$p$-saturated
formations. In this paper, we shall give an interesting example of saturated formation ${\cal F}$ which is expressible by
${\cal F}={\cal M}{\cal H},$ where ${\cal M}$ and ${\cal H}$ are both non-$p$-saturated formations for all $p\in \pi ({\cal
F}).$ We then prove that if the product formation ${\cal F}={\cal M}{\cal H}$ of two formations ${\cal M}$ and ${\cal H}$
is a one-generated $w$-saturated formation with ${\cal F}\not ={\cal H}$, then ${\cal M}$ is also a $w$-saturated formation.
By using this result, we shall answer two problems proposed by Skiba and Shemetkov.
Received: 12 October 2001 / Revised version: 11 February 2002 相似文献