On the Decomposition Theorems for C∗-Algebras

Elliott dimension drop interval algebra is an important class among all C*-algebras in the classification theory.Especially,they are building stones of AHD alge...     

Going-down functors, the Künneth formula, and the Baum-Connes conjecture

We study the connection between the Baum-Connes conjecturefor a locally compact group G with coeefficient A and the Künnethformula for the K-theory of tensor products by the corresponding crossedproduct . The main tool for this is obtained by an application ofa general reduction procedure which allows us to analyze certain functorsconnected to the topological K-theory of a group in terms of their restrictionsto compact subgroups. We also discuss several other interestingapplications of this method, including a general extension result for theBaum-Connes conjecture.     

Representable K-Theory for σ-C*-algebras

We define a version of K-theory on the category of -C ^*-algebras (countable inverse limits of C ^*-algebras). Our theory is homotopy invariant, has long exact sequences and a Milnor sequence, and satisfies Bott periodicity. On C ^*-algebras it gives the ordinary K-theory, and on the space of continuous functions on a countable direct limit X of compact Hausdorff spaces, it gives the representable K-theory of X. (We do not claim that our theory is in general a representable functor.) We also define an equivariant version, and discuss several related groups.Partially supported by a National Science Foundation Postdoctoral Fellowship.     

Constructions and Dévissage in Hermitian K-Theory

We first give the good definition of the Hermitian K-theory of an exact category with duality. Then we prove a Dévissage theorem which allows us to compare the Hermitian K-theory of a number field with the Hermitian K-theory of its integers.     

K-Theory of Semi-local Rings with Finite Coefficients and étale Cohomology

Let A be a commutative semi-local ring containing 1/2. We construct natural isomor-phisms

A K¨unneth Formula for Finite Sets*

In this paper, the authors define the homology of sets, which comes from and contains the ideas of path homology and embedded homology. Moreover, A K¨unneth formula for sets associated to the homology of sets is given.     

On the classification of certain real rank zero C*-algebras

In this paper,we give a classification of real rank zero C^*-algebras that can be expressed as inductive limits of a sequence of a subclass of Elliott-Thomsen algebras C.     

AF C*-代数中的Lie理想

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.     

Hilbert C*模及其有界模映射

设E为C^*代数A上可数生成的Hilbert模,B(E)为E上有界模映射全体,则B(E)保距同构于K(E)的左乘子,其中K(E)为E上“紧”模映射全体。当A为无限维本原C^*代数且E为自对偶模,则E为代数有限生成。     

Hilbert C*模上的Gabor酉系统

本文引入了Hilbert C*-模上的Gabor酉系统的概念,研究了它的基本性质,证明了膨胀定理,并给出某个酉系统的两个正规框架向量不相交的等价条件.     

A Characterization of the Standard Tori in C2 as Compact Lagrangian ξ-Submanifolds*

In this paper, the authors give a characterization theorem for the standard tori S¹(a) × S¹(b), a, b > 0, as the compact Lagrangian ξ-submanifolds in the two-dimensional complex Euclidean space C² , and obtain the best version of a former rigidity theorem for compact Lagrangian ξ-submanifold in C² . Furthermore, their argument in this paper also proves a new rigidity theorem which is a direct generalization of a rigidity theorem by Li and Wang for Lagrangian self-shrinkers in C².     

Convergence of Gradient Algorithms for Nonconvex C1+α Cost Functions*

This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting. A class of stochastic momentum methods, including stochastic gradient descent, heavy ball and Nesterov’s accelerated gradient,is analyzed in a general framework under mild assumptions. Based on the convergence result of expected gradients, the authors prove the almost sure convergence by a detailed discussion of the effects of momentum and the number of upcrossings. It is worth noting that there are not additional restrictions imposed on the objective function and stepsize.Another improvement over previous results is that the existing Lipschitz condition of the gradient is relaxed into the condition of H¨older continuity. As a byproduct, the authors apply a localization procedure to extend the results to stochastic stepsizes.     

C1,α-partial Regularity of Nonlinear Parabolic Systems

We prove C^{1,α}-partial regularity of weak solution of nonlinear parabolic systems u^i_t - D_αA^α_i(x, t, u, Du) = B_i(x, t, u, Du), \quad i=1,…, N under the main assumption that A^α_i and B_i, satisfy the natural growth condition.     

Hilbert C*-模中框架的擦除和刻画（英文）

本文给出了两个充分必要条件,使得当Hilbert C^*-模中的框架擦除一个元素后其剩余部分可构成一个新框架.此外给出了Hilbert C^*-模中框架的几个新刻画,与此同时,给出了关于该主题的一个已有结果的完整证明.     

Hilbert C*-模算子代数上Lie导子的标准形式

设A是一个含单位e的交换C^*-代数,M是一个满的Hilbert A-模.M到自身的有界A-线性映射全体构成的代数记作End_A（M）,M到A的有界A-线性映射全体组成的集合记作M'.在本文中,我们证明了如果存在x₀∈M,f₀∈M'使得f₀（x₀）=e,那么End_A（M）上的每个A-线性的Lie导子δ都是标准的.即δ可以分解成d+τ的形式,其中d是一个A-线性的导子,τ是一个A-线性的中心值映射,并且对任意的A,B∈End_A（M）,有τ（AB）=τ（BA）.     

C*代数l上的左模的半双线性型的稳定性

本文分别研究了 C^*-代数l上的单位左模和具有实阶零性质的CC^*代数l上的单位左模的半双线性型的 Hyers-Ulam 稳定性.     

Balanced path decomposition of λ K n,n and λ K n,n *

Let P _k denote a path with k edges and λ K _n,n denote the λ-fold complete bipartite graph with both parts of size n. In this paper, we obtain the necessary and sufficient conditions for λ K _n,n to have a balanced P _k -decomposition. We also obtain the directed version of this result.