A note on noncommutative moment problems

Noncommutative moment problems for C*-algebras are studied. We generalize a result of Hadwin on tracial states to nontracial case. Our results are applied to obtain simple solutions to moment problems on the square and the circle as well as extend the positive unital functionals from a (discrete) complex group algebra to states on the group C*-algebra.     

Local automorphisms and derivations on certain -algebras

It is shown that continuous -local derivations on -algebras are derivations and surjective -local *-automorphisms on prime -algebras or on -algebras such that the identity element is properly infinite are *-automorphisms.

     

The -PIP and integrability of a single function

Two examples are given that answer in the negative the following question asked by E. M. Bator: If is bounded and weakly measurable and for each in there is a bounded sequence in such that a.e., does it follow that is Pettis integrable?

     

A separable non-remainder of

We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.

     

基于完备BR0-代数的全蕴涵三I算法

研究了基础$BR_0$-代数的性质和基于完备基础$BR_0$-代数的全蕴涵三I算法,对一般蕴涵算子给出了三I算法解存在的一个充分条件,并将结果应用于$R_0$-单位区间$\overline{W}$,不但极大的简化了$R_0$-单位区间$\overline{W}$的$R_0$-型$\alpha$-三I算法结果的证明,而且使其证明过程与相应的模糊命题演算系统结合起来,说明了$R_0$-型三I算法是与$B{\cal L}^*$系统相匹配的模糊推理方法.     

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the -algebra of a CKT family, and prove a universality theorem for -algebras generated by these families. In both cases, the -algebras generated by quiver algebras play the universal role.

     

$*$-双单型$A \omega^2$-半群的同构定理

在本文中,我们研究了满足条件$D^*=D(~)$的*-双单型$A\omega^2$-半群的同构,给出了它们之间的同构定理.     

{Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces

Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)"(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$.     

Transitive families of projections in factors of type

We introduce a notion of transitive family of subspaces relative to a type factor, and hence a notion of transitive family of projections in such a factor. We show that whenever is a factor of type and is generated by two self-adjoint elements, then contains a transitive family of projections. Finally, we exhibit a free transitive family of projections that generate a factor of type .

     

On the correlations of directions in the Euclidean plane

Let denote the repartition of the -level correlation measure of the finite set of directions , where is the fixed point and is an integer lattice point in the square . We show that the average of the pair correlation repartition over in a fixed disc converges as . More precisely we prove, for every and , the estimate

We also prove that for each individual point , the -level correlation diverges at any point as , and we give an explicit lower bound for the rate of divergence.

     

A continuity property of multivariate Lagrange interpolation

Let be a sequence of interpolation schemes in of degree (i.e. for each one has unique interpolation by a polynomial of total degree and total order . Suppose that the points of tend to as and the Lagrange-Hermite interpolants, , satisfy for all monomials with . Theorem: for all functions of class in a neighborhood of . (Here denotes the Taylor series of at 0 to order .) Specific examples are given to show the optimality of this result.

     

A reflexivity problem concerning the

Let be a compact Hausdorff space and let be a separable Hilbert space. We prove that the group of all order automorphisms of the -algebra is algebraically reflexive.

     

Katetov's problem

In 1948 Miroslav Katetov showed that if the cube of a compact space satisfies the separation axiom T then must be metrizable. He asked whether can be replaced by in this metrization result. In this note we prove the consistency of this implication.

     

$\mathbb{Z}^{k}$-作用一维子系统的Lipschitz跟踪性

本文主要研究了$\mathbb{Z}^{k}$-作用一维子系统的跟踪性质. 文中运用两种等价的方式引入了$\mathbb{Z}^{k}$-作用一维子系统的伪轨以及跟踪性的概念. 对于一个闭黎曼流形上的光滑$\mathbb{Z}^{k}$-作用$T$, 我们通过诱导的非自治动力系统提出了Anosov方向的概念. 借助Bowen几何的方法, 我们证明了$T$沿着任意Anosov方向具有Lipschitz跟踪性.     

右型A半群的F-覆盖

A right adequate semigroup of type F is defined as a right adequate semigroup which is an F-rpp semigroup. A right adequate semigroup T of type F is called an F-cover for a right type-A semigroup S if S is the image of T under an L＊-homomorphism. In this paper, we will prove that any right type-A monoid has F-covers and then establish the structure of F-covers for a given right type-A monoid. Our results extend and enrich the related results for inverse semigroups.     

完全图的Cantesian积的L(2,1)-圆标定

For positive integers j and k with j ≥ k, an L（j, k）-labeling of a graph G is an assignment of nonnegative integers to V（G） such that the difference between labels of adjacent vertices is at least j, and the difference between labels of vertices that are distance two apart is at least k. The span of an L（j, k）-labeling of a graph G is the difference between the maximum and minimum integers it uses. The λj, k-number of G is the minimum span taken over all L（j, k）-labelings of G. An m-（j, k）-circular labeling of a graph G is a function f ： V（G） →{0, 1, 2,..., m - 1} such that ｜f（u） - f（v）｜m ≥ j if u and v are adjacent; and ｜f（u） - f（v）｜m 〉 k ifu and v are at distance two, where ｜x｜m = min{｜xl｜, m-｜x｜}. The minimum integer m such that there exists an m-（j, k）-circular labeling of G is called the σj,k-number of G and is denoted by σj,k（G）. This paper determines the σ2,1-number of the Cartesian product of any three complete graphs.     

Small Covers over a Product Space

A small cover is a closed manifold $M^{n}$ with a locally standard $(\Bbb{Z}_{2})^{n}$-action such that its orbit space is a simple convex polytope $P^{n}$. Let $\Delta^{n}$ denote an $n$-simplex and $P(m)$ an $m$-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space $\Delta^{n_1}\times \Delta^{n_2} \times P(m)$, where $n_1$ is odd.     

On a generalized corona problem on the unit disc

Let . We give a sufficient condition on the size of a function in order for it to be in the ideal generated by . In particular, this improves Cegrell's result on this problem.

     

拟对角扩张Cuntz半群的某些性质

设O→J→A→B→O是一个拟对角扩张.作者证明如果J和B具有Cuntz半群的某些性质,则A也具有相同的半群性质.