算子代数上的Lie可导映射

设A为有单位且包含一非平凡幂等元的环,M为A双模.称δ:A→M为Lie可导映射(无可加或连续假设),若δ([A,B])=[δ(A),B]+[A,δ(B)],(?)A,B∈A.在一定条件下该文证明了Lie可导映射δ具有形式δ(A)=τ(A)+f(A),其中r:A→M是可加导子,f是从A到M的中心且满足f([A,B])=0,(?)A,B∈A的映射.由此刻画了因子von Neuamnn代数和套代数上的Lie可导映射.     

A counter-example to a conjecture of Friedland

In 1982, S. Friedland proved that a bounded linear operator A on a Hilbert space is normal if and only if (αI + A + A*)² ≧ AA* − A*A ≧ −(αI + A + A*)² for all real α. And he conjectured the inequality (αI + A + A*)² ≧ AA* − A*A for all real α will imply that A*A − AA* ≧ 0, i.e., A is hyponormal. But his conjecture is incorrect. In this note I’ll give a counter-example for his conjecture.     

全流通格局下沪市主并上市公司并购绩效研究

以全流通格局下2007年发生并购的56家上市公司为样本,应用超常收益方法对沪市主并上市公司并购的绩效进行实证研究.结果表明:主并上市公司并购后绩效呈上升趋势;在横向并购、纵向并购和混合并购三种方式中,纵向并购的效果优于横向并购和混合并购,而横向并购与混合并购对绩效的影响区别不明显.     

因子von Neumann代数上的非线性混合ξ-Jordan三重可导映射

设A是一个的因子von Neumann代数.我们证明了每一个非线性混合ξ-Jordan（ξ≠0，-1）三重可导映射φ：A → A都是可加的*-导子，且对任意的A ∈ A，有φ（ξA）=ξφ（A）.     

On strongly-non-reflexive groups

A strong negative answer is given to the old question of whether every dual group is reflexive. Using ◊_ω1 a groupA is constructed so thatA, A*, A**, andA*** are weakly ω₁-separable groups of cardinalityω ₁ andA* is not isomorphic toA***. Research partially supported by NSF Grant No. DMS-8400451. Research partially supported by NSERC Grant No. A8948.     

Universal C*-algebras defined by completely bounded unital homomorphisms

Suppose A is a unital C*-algebra and r 1.In this paper,we define a unital C*-algebra C_(cb)*(A,r) and a completely bounded unital homomorphism α_r:A → C_(cb)*(A,r)with the property that C_(cb)*(A,r)=C*(α_r(A))and,for every unital C*-algebra B and every unital completely bounded homomorphism φ:A→ B,there is a(unique)unital *-homomorphism π:C_(cb)*(A,r)→B such thatφ=πoα_r.We prove that,if A is generated by a normal set {t_λ:λ∈Λ},then C_(cb)*(A,r)is generated by the set {α_r(t_λ):λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C_(cb)*(A,r)we obtain that,if Β is a unital C*-algebra that can be embedded into A,then C_(cb)*(B,r)can be naturally embedded into C(cb)*(A,r).We give characterizations of C_(cb)*(A,r)for some special situations and we conclude that C_(cb)*(A,r)will be "nice" when dim(A)≤ 2 and "quite complicated" when dim(A)≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C_(cb)*(A,r).We also define and study some analogous of C_(cb)*(A,r).     

On the parity of generalized partition functions II

Let A = {а 1 < a 2 < ...} be a set of positive integers and A(x) its counting function. Let us denote the number of partitions of n with parts in A by p( A , n). Improving on two preceding papers jointly written with I.Z. Ruzsa and A. Sárközy (J. Number Theory, 1998) and with A. Sárközy (Millennial Conference on Number Theory, May 2000, Urbana, Illinois, U.S.A.), it is shown that there exists a set A satisfying A(x) > c xlog log x/ (log x) 1/3 , c<0, such that, for n large enough, p( A ; n) isalways even.     

The Group of Outer Automorphisms and the Picard Group of an Algebra

The primary goal of this work is to develop a strategy to compute Pic_K(A) and Out_K(A) where A is a finite-dimensional algebra over a field K. The basic idea is to put the normal subgroup Inn^*(A) of the inner automorphisms of A induced by elements of 1 + J(A), as a common denominator in the fraction Aut_K(A) / Inn(A). The new numerator Aut_K(A)/Inn^*(A) and the new denominator Inn(A)/Inn^*(A) are much easier to deal with than the original Aut_K(A) and Inn(A). The main ingredient to study Out(A) is now the appearance of an Abelian group Ch(, K), the group of acyclic characters of the quiver of A, that can be completely calculated. We show how to apply these results to compute the Picard group of a split finite-dimensional algebra in several cases.     

A set of maps from K to EndA(l2(A)) isomorphic to EndA(K)(l2(A(K))). Applikations

Let A be a C^*-algebra, K be a compact space, A(K) be the C^*-algebra of all continuous maps from K into A, 1₂(A) be the standard countably generated Hilbert A-module. We investigate a set of maps from K into End_A(1₂(A)), which is isomorphic to End_A(K)(1₂(A(K))). We describe the subsets which are isomorphic to End_fA(K) ^*(1₂(A(K))). GL_A(K)(1₂(A(K))) and GL_fA(K) ^*(1₂(A(K))), respectively. As an application we deduce a criterion for the self-duality of 1₂(A) in the commutative case.     

BMO ESTIMATES FOR MULTILINEAR FRACTIONAL INTEGRALS

In this paper,the authors prove that the multilinear fractional integral operator T A 1,A 2 ,α and the relevant maximal operator M A 1,A 2 ,α with rough kernel are both bounded from L p (1 p ∞) to L q and from L p to L n/(n α),∞ with power weight,respectively,where T A 1,A 2 ,α (f)(x)=R n R m 1 (A 1 ;x,y)R m 2 (A 2 ;x,y) | x y | n α +m 1 +m 2 2 (x y) f (y)dy and M A 1,A 2 ,α (f)(x)=sup r0 1 r n α +m 1 +m 2 2 | x y | r 2 ∏ i=1 R m i (A i ;x,y)(x y) f (y) | dy,and 0 α n, ∈ L s (S n 1) (s ≥ 1) is a homogeneous function of degree zero in R n,A i is a function defined on R n and R m i (A i ;x,y) denotes the m i t h remainder of Taylor series of A i at x about y.More precisely,R m i (A i ;x,y)=A i (x) ∑ | γ | m i 1 γ ! D γ A i (y)(x y) r,where D γ (A i) ∈ BMO(R n) for | γ |=m i 1(m i 1),i=1,2.     

无限箭图的同调群

对任意箭图Q,我们研究路代数A=kQ的Hochschild同调群H_n(A)和同调群Tor_n^Ae(A,A),其中A^e是代数A的包络代数。在本文中,我们具体地给出了各次同调群和Hochschild同调群。     

ON ANTISIMPLE GAMMA RINGS

ABSTRACT

In this note, we define the antisimple radical, A(M), of a Γ-ring M. A(M) is shown to be a special radical, and two characterizations of antisimple rings due to Szész are extended to Γ-rings. If R is the right operator ring of M, then A(R)* = A(M), where A(R) is the antisimple radical of R. If m,n are positive integers, then A(M_mn) = (A(M))_mn, where M_mn denotes the group m x n matrices over M, considered as a Γ_nm -ring with the operations of matrix addition and multiplication.     

S-Cohn–Jordan Extensions

Let a monoid S act on a ring R by injective endomorphisms and A(R; S) denote the S-Cohn–Jordan extension of R. A series of results relating properties of R and that of A(R; S) are presented. In particular it is shown that: (1) A(R; S) is semiprime (prime) iff R is semiprime (prime), provided R is left Noetherian; (2) if R is a semiprime left Goldie ring, then so is A(R; S), Q(A(R; S)) = A(Q(R); S) and udim R = udim A; (3) A(R; S) is semisimple iff R is semisimple, provided R is left Artinian. Some applications to the skew semigroup ring R#S are given.     

Rings with all modules residually finite

Define a ringA to be RRF (resp. LRF) if every right (resp. left) A-module is residually finite. Refer to A as an RF ring if it is simultaneously RRF and LRF. The present paper is devoted to the study of the structure of RRF (resp. LRF) rings. We show that all finite rings are RF. IfA is semiprimary, we show thatA is RRF ⇔A is finite ⇔A is LRF. We prove that being RRF (resp. LRF) is a Morita invariant property. All boolean rings are RF. There are other infinite strongly regular rings which are RF. IfA/J(A) is of bounded index andA does not contain any infinite family of orthogonal idempotents we prove:

自伴标准算子代数上强保持k-斜交换性映射的刻画

令H是维数大于2的复Hilbert空间,A是H上自伴标准算子代数.对于给定的正整数k≥1,H上算子A与B的k-斜交换子递推地定义为_*[A,B]_k=_*[A,_*[A,B]_k-1],其中_*[A,B]₀=B,_*[A,B]₁=AB-BA^*.设k≥4,φ是A上的值域包含所有一秩投影的映射.本文证明了φ满足_*[φ（A）,φ（B）]_k=_*[A,B]_k对任意A,B∈A都成立的充分必要条件是φ（A）=A对任意A∈A都成立,或φ（A）=-A对任意A∈A都成立.当k是偶数时后一情形不出现.     

Von Neumann Algebras and Hilbert Quantales

When A is a von Neumann algebra, the set of all weakly closed linear subspaces forms a Gelfand quantale, Max_w A. We prove that Max_w A is a von Neumann quantale for all von Neumann algebras A. The natural morphism from Max_w A to the Hilbert quantale on the lattice of weakly closed right ideals of A is, in general, not an isomorphism. However, when A is a von Neumann factor, its restriction to right-sided elements is an isomorphism and this leads to a new characterization of von Neumann factors.     

企业战略对并购行为的影响和潜在机制

为探究企业战略风险度和偏离度对并购行为的影响,本文以沪深A股2010~2017为样本数据,基于Logit和Possion模型对企业战略与并购行为的影响机制进行实证检验。结果显示:企业战略风险度与并购行为显著正相关,表明企业战略越是风险偏好型的企业,其并购倾向越高,并购次数越多;企业战略偏离度与并购行为显著负相关,表明企业战略越是偏离同行常规战略的企业,其并购倾向越低,并购次数越少。进一步研究表明,完善的内部控制、较高的薪酬激励和聘请稳健的高管能够有效约束由企业战略引起的过度并购和并购不足行为,促进并购行为合理化。本文基于企业战略视角研究并购倾向和并购次数,有助于理解并购行为形成的内在机制,同时,对上市公司并购行为的治理和风险管控亦提供了新的线索和证据。     

A helly-number fork-almost-neighborly sets

It is possible to prove the following “Helly-type” thorem fork-almost-neighborly sets. Theorem.A ⊆R ^d is k-almost-neighborly if and only if every 2d+1 member subset of A is k-almost-neighborly. Moreover, if A ⊆bdry conv A, then A is k-almost-neighborly if and only if every 2d member subset of A is k-almost-neighborly. Each bound is best possible.     

The conductor of one-dimensional gorenstein rings in their blowing-up

Let (A,M) be a local, one-dimensional, Cohen-Macaulay ring of multiplicity e=e(A)>1 and Hilbert function H(A). Let I=Ann_A (B/A) be the conductor of A in its blowing up B. Northcott and Matlis have proved that if the embedding dimension emdim A of A is 2 then I=M^e−1 [3; Corollary 13.8]. If emdim A>2 little is know about I. In [6] and [7] I is computed when the associated graded ring G(A) is reduced (in this case B in the integral closure of A). In this paper we compute I when A is Gorenstein. There are in general upper and lower bounds for I in terms of a power of M and we start discussing when these bounds are attained. In particular we show that in the extremal situation I=M^e−1 one has emdimA=2 (thus inverting the result of Northcott and Matlis). Then we consider the case of Gorenstein rings. We prove that if G(A) in Gorenstein then I=M^ϑ where ϑ=Min{n‖H(n)=e}. If more generally A is Gorenstein then I⊂M² or emdim A=e(A)=2. When A is the local ring of a curve at a singular point p we get, as a consequence of this last result a proof of the following conjecture of Catanese which has interesting geometric applications [1]: if the conductor J of A in its normalization is not contained in M² then p is a node.