C*-Isomorphisms Associated with Two Projections on a Hilbert C*-Module*

Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C^*-isomorphisms associated with two projections by introducing the matched triple and the semi-harmonious pair of projections. A triple (P, Q, H) is said to be matched if H is a Hilbert C^*-module, P and Q are projections on H such that their infimum P ∧ Q exists as an element of L(H), where L(H) denotes the set of all adjointable operators on H. The C^*-subalgebras of L(H) generated by elements in {P - P ∧ Q, Q - P ∧ Q, I} and {P, Q, P ∧ Q, I} are denoted by i(P, Q, H) and o(P, Q, H), respectively. It is proved that each faithful representation (π, X) of o(P, Q, H) can induce a faithful representation (π, X e) of i(P, Q, H) such that e π(P - P ∧ Q) = π(P) - π(P) ∧ π(Q),eπ(Q - P ∧ Q) = π(Q) - π(P) ∧ π(Q).When (P, Q) is semi-harmonious, that is, R(P + Q) and R(2I - P - Q) are both orthogonally complemented in H, it is shown that i(P, Q, H) and i(I - Q, I - P, H) are unitarily equivalent via a unitary operator in L(H). A counterexample is constructed, which shows that the same may be not true when (P, Q) fails to be semi-harmonious. Likewise, a counterexample is constructed such that (P, Q) is semi-harmonious, whereas (P, I - Q) is not semi-harmonious. Some additional examples indicating new phenomena of adjointable operators acting on Hilbert C^*-modules are also provided.     

Two Commuting Involutions Fixing RP1(2m + 1) S RP2(2m + 1)*

Let Z₂ denote a cyclic group of 2 order and Z₂² = Z₂ ×Z₂ the direct product of groups. Suppose that (M, Φ) is a closed and smooth manifold M with a smooth Z₂² -action whose fixed point set is the disjoint union of two real projective spaces with the same dimension. In this paper, the authors give a sufficient condition on the fixed data of the action for (M, Φ) bounding equivariantly.     

K-theory for rickart C*-algebras

We give an explicit index map for any properly infinite closed ideal of a Rickart C ^*-algebra. This generalizes Olsen's work on von Neumann algebras. We use our results to compute the topological and the algebraic K ₁-groups of any quotient algebra of a Rickart C ^*-algebra.     

On the ordered K0 group of a simple C*-algebra

It is shown that any countable simple and unperforated partially ordered Abelian group with order unit, paired in an arbitrary way with a compact metrizable Choquet simplex, occurs as the K₀group of a simple unital ^*-algebra which is the inductive limit of a sequence of subhomogeneous ^*-algebras of a particularly simple form.     

Hom-derivations in C*-ternary Algebras

In this paper, we introduce and solve the following additive (ρ₁, ρ₂)-functional inequalities ||f(x+y+z)-f(x)-f(y)-f(z)|| ≤ ||ρ₁(f(x+z)-f(x)-f(z))||+||ρ₂(f(y+z)-f(y)-f(z))||, where ρ₁ and ρ₂ are fixed nonzero complex numbers with|ρ₁|+|ρ₂|< 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the above additive (ρ₁, ρ₂)-functional inequality in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of hom-derivations in C^*-ternary algebras.     

Hilbert C~*-模中g-框架的一些性质

本文运用算子理论方法,给出Hilbert C~*-模中g-框架的一些性质并讨论g-框架的扰动性,得到g-框架的和的一些刻画,所得结果推广和改进了已有的结果.     

W~*-三元算子环的摄动

本文证明了:如果两个W~*-三元算子环V和W的cb距离d_(cb)(V,W)很小的时候,其连接冯·诺依曼代数之间的距离也很小.还证明了:和内射的W~*-三元算子环靠的很近的W~*-三元算子环也是内射的.对具有r性质和McDuff性质的W~*-三元算子环,类似的结论也成立.     

基础R0-代数的性质及在L*系统中的应用

研究了王国俊教授建立的模糊命题演算的形式演绎系统L^*和与之在语义上相关的R₀-代数,提出了基础R₀-代数的观点并讨论了其中的一些性质,在将L^*系统中的推演证明转化为相应的R₀-代数中的代数运算方面作了一些尝试,作为它的一个应用,证明了L^*系统中的模糊演绎定理。     

在奇次Legendre多项式零点上的（0，2）*插值

设Ｐ_ｎ表示ｎ次Ｌｅｓｅｎｄｒｅ多项式，本文考虑多项式（１－ｘ²）Ｐ_ｎ．（ｘ）／ｘ（ｎ为奇数）零点上的（０，２）^*插值问题，得到了这种插值的正则性，显式表达式及收敛性．     

The Atiyah-Segal completion theorem for C*-algebras

We generalize the Atiyah-Segal completion theorem to C ^*-algebras as follows. Let A be a C ^*-algebra with a continuous action of the compact Lie group G. If K _* ^G (A) is finitely generated as an R(G)-module, or under other suitable restrictions, then the I(G)-adic completion K _* ^G (A) is isomorphic to RK _*([A C(EG)]^G), where RK _* is representable K-theory for - C ^*-algebras and EG is a classifying space for G. As a corollary, we show that if and are homotopic actions of G, and if K _*(C ^* (G,A,)) and K _*(C ^* (G,A,)) are finitely generated, then K _*(C ^*(G,A,))K_*(C ^* (G,A,)). We give examples to show that this isomorphism fails without the completions. However, we prove that this isomorphism does hold without the completions if the homotopy is required to be norm continuous.This work was partially supported by an NSF Graduate Fellowship and by an NSF Postdoctoral Fellowship.     

Rieffel projections in certain transformation group C*-algebras

LetA be the transformation groupC ^*-algebra associated with an arbitrary orientation-preserving homeomorphism of . ThisC ^*-algebra contains an infinite family of projections, called Rieffel projections, each of which generates theK ₀-groupK ₀(A). Although these projections must beK-theoretically equivalent, it is easy to see that most are not Murray-von Neumann equivalent. The mystery of how large the matrix algebra must be to implement theK-theory equivalence, is solved by explicitly constructing the equivalence in the smallest possible algebra:A with unit adjoined.Partially supported by NSF Grant DMS 8901923.     

A bott periodicity map for crossed products of C*-algebras by discrete groups

A generalization is given of the canonical map from a discrete group into K ₁ of the group C ^*-algebra. Our map also generalizes Rieffel's construction of a projection in an irrational rotation C ^*-algebra.     

非单C~*-代数α-比较性的等价刻画

给出非单C~*-代数α-比较性的等价刻画:当每个τ∈QT(■H)均为忠实时,■具有α-比较性,当且仅当对于任意的〈a〉,〈b〉∈Cu(■)且∝,若α·d_τ(a)≤在Cu(■)中成立;一般地,当QT(■H)≠Φ时,■具有α-比较性,当且仅当对于任意的,∈Cu(■),若存在η>0,使得d_τ(α)≤(α~(-1)-η)d_τ(b)(_τ∈QT(■H)),则≤在Cu(■)中成立.     

IRRATIONAL ROTATION c^＊—ALGEBRA FOR GROUPOID c^＊—ALGEBRA

ＩＲＲＡＴＩＯＮＡＬＲＯＴＡＴＩＯＮｃ－ＡＬＧＥＢＲＡＦＯＲＧＲＯＵＰＯＩＤｃ－ＡＬＧＥＢＲＡ￥ＣＨＥＮＸＩＡＯＭＡＮ；ＸＵＱＩＮＧＸＩＡＮＧ；ＸＵＳＨＥＮＧＺＨＩ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，Ｆ＇ｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈ...     

单C~*-代数α-比较性的一种等价刻画

给出C~*-代数α-比较性的等价刻画:对于单的含单位元的稳定有限的C~*-代数A而言,A具有α-比较性,当且仅当对于任意的a,b∈W(A),若α·d_r(a)d_τ(b)(_τ∈QT(A)),则a≤b在Cuntz半群W(A)中成立.利用此刻画,证明了具有α-比较性的C~*-代数一定具有弱比较性;若A具有α-比较性,其中α=m+1,则A具有正元的强迹m-比较性;对于满足Kirchberg-R?rdam条件的C~*-代数,E-稳定、严格比较、α-比较性(α=m+1)、强迹m-比较性、弱比较性以及局部弱比较性彼此等价;若α:=inf{α′∈(1,∞)|A具有α′-比较}∞,则A具有α-比较性.     

Relative K homology and C* algebras

Let A be a separable nuclear C ⁺ algebra with unit. Let be a closed two-sided ideal in A. A relative K homology group K ⁰(A,) is defined. Closely related are topological definitions of properly supported K homology and of compactly supported relative K homology. Applications are to indices of Toeplitz operators and existence of coercive boundary conditions for elliptic differential operators.     

On Representations Associated with Completely n-Positive Linear Maps on Pro-C^＊-Algebras

It is shown that an n × n matrix of continuous linear maps from a pro-C^＊-algebra A to L（H）, which verifies the condition of complete positivity, is of the form [V^＊TijФ（·）V]^n i,where Ф is a representation of A on a Hilbert space K, V is a bounded linear operator from H to K, and j=1,[Tij]^n i,j=1 is a positive element in the C^＊-algebra of all n×n matrices over the commutant of Ф（A） in L（K）. This generalizes a result of C. Y.Suen in Proc. Amer. Math. Soc., 112（3）, 1991, 709-712. Also, a covariant version of this construction is given.     

多重C~*-动力系统在Hilbert C~*-模上的膨胀

研究了多重C~*-动力系统在Hilbert C~*-模上表示的膨胀.设(A,α)是一个多重C~*-动力系统,(π,T,E)是(A,α)的行压缩协变表示,证明了存在(π,T,E)的等距膨胀(ρ,V,F).     

L 1→ L q Poincaré Inequalities for 0 < q < 1 Imply Representation Formulas

Given two doubling measures μ and ν in a metric space (S, ρ) of homogeneous type, let B ₀⊂S be a given ball. It has been a well-known result by now (see [1–4]) that the validity of an L ¹→L ¹ Poincaré inequality of the following form: for all metric balls B⊂B ₀⊂S, implies a variant of representation formula of fractional integral type: for ρ-a.e. x∈B ₀, One of the main results of this paper shows that an L ¹ to L ^q Poincaré inequality for some 0 < q < 1, i.e., for all metric balls B⊂B ₀, will suffice to imply the above representation formula. As an immediate corollary, we can show that the weak-type condition, also implies the same formula. Analogous theorems related to high-order Poincaré inequalities and Sobolev spaces in metric spaces are also proved. Received December 27, 2000, Accepted May 28, 2001