纯无限单C*-代数的扩张代数的K-理论

给出了纯无限单的C*-代数A通过K的扩张代数E的K-理论的一种刻划.证明了K0(E)等于E中所有无限投影的Murry-von Neumann等价类所成的交换群,K1(E)等于E中酉元的同伦等价类所成的交换群.作为一个应用,最后给出了A中酉元可提升的等价条件,其中K为可分无限维Hilbert空间上紧箅子全体所成的C*-代数.     

C~*标准代数中效应的序列同构

主要借助于C~*标准算子代数中的有限秩算子对一般的效应元进行刻画.证明了C~*标准算子代数A的效应代数E(A)上的每个序列自同构和自同构ψ都具有形式ψ(A)=UAU~*,其中A∈E(A),U为酉算子或反酉算子.     

C*代数上保持不定正交性的线性映射

设A和B是含单位元的C*代数,s∈A和t∈B是可逆自伴元.对任意的x∈A及z∈B,定义x+=s-1x*s,z+=t-1z*t.假定A是实秩零的并且φA→B是有界线性满射.证明了对任意的x,y∈A,x+y=0 φ(x)+φ(y)=0且xy+=0φ(x)φ(y)+=0都成立的充要条件是φ(1)可逆,φ(1)+φ(1)=φ(1)φ(1)+∈Z(B)(B的中心),并且存在从A到B上的满+同态ψ,使得对所有的x∈A都有φ(x)=φ(1)ψ(x)成立.对于一般C*代数上保正交性的线性映射φ,在假定φ(1)可逆的条件下,也得到类似的结果.     

关于双曲型方程的狄里赫利问题的两点注记

1°在文献[1]中D.Bourgin与R.Duffin研究了絃振动方程在矩形区域上可适定的狄里赫利问题,他们指出对于问题:若设(i)a=T/s为K阶代数无理数,(ii)φ(x),φ_1(x)∈C~(K+4)[0≤x≤s],ψ(t),ψ_1(t)∈C~(K+4)[0≤t≤T],φ(0)=φ(s)=φ_1(0)=φ_1(s)=ψ(T)=ψ_1(0)=ψ_1(T)=0,则定解问题(A)存在唯一解y(x,t)∈C~2[0≤x≤s,0≤t≤T]。他们的结果系利用代数数论中Liouville定理。由于Liouville定理已被Roth在1955年改进成最佳形式,     

纯无限单C*-代数的扩张代数的K-理论Ⅱ

给出了有单位元的纯无限单的C*-代数A通过K的扩张代数E的K-理论的一种刻画.证明了K0(E)同构于E中所有具有无限余投影的无限投影的Murry-yon Neumann等价类全体所成的交换群,它还同构于上述投影的同伦等价类或酉等价类全体所成的交换群.还证明了对扩张代数E中的任·满的正元a,存在元索z ∈E,使得x*ax=1,其中K为可分无限维Hilbert空间上紧算子全体所成的C*一代数.     

C~* -代数上完全正映射的刻画

本文给出C* -代数之间完全正映射的刻画,证明:如果A,B是有单位元的C*-代数,则映射Φ:A→B为完全正映射当且仅当存在保单位*-同态πA:A→B(K)、等距* -同态πB:B→B(H)及有界线性算子V:H→K,使得πB(Φ(1))=V*V 且■a∈A,都有πB(Φ(a))=V*π(a)V.作为推论,得到著名的Stinespring膨胀定理.     

E*-酉范畴逆半群的一个表示定理

本文,我们对带零逆半群定义了0-对偶预同态的概念,并且用0-对偶预同态刻画了E*-酉范畴逆半群。     

连续信息代数

给出基于自由域信息代数和带论域信息代数上的连续性概念.证明在城集格有最大元的情况下,两种连续性之间是相互对应的.定义了连续信息代数之间的连续映射的概念,证得:若(φ,D),(ψ,E)都是强连续的信息代数.则([φ→ψ]c,D×E)也是强连续的.     

余代数的co-Frobenius扩张及其同调性质

一个余代数对(C,D)连同一个余代数同态α:C→D说是右co-Frobenius的,若且C作为右D-余模是有限余生成内射的。一个有限维余代数C是co-Frobenius余代数,恰当(C,k)是右co-Frobenius对。对于co-Frobenius对(C,D),其中(ⅰ)C,D都是co-Frobenius余代数,(ⅱ)C是有限维的并可嵌入到D,[5]中对Frobenius(环)扩张所论证的相对同调性质可以对偶过来。这些是(1)C对于D的相对右整体维数Dim(C,D)是0或∞(2)对于任意C-余模V,V的C-余维数cd_C(V)等于它的D-余维数cd_D(V),如果下列条件之一成立:(ⅰ)V是(C,D)-内射的,(ⅱ)cd_c(V)<∞。还得到了关于V在C及D上(同调)维数的部分结果。     

BE-代数上的模与半本原BE-代数

文[1]中引进了BE—代数以后,文[2]给出了这种代数的同态、同构定理,本文在[1]、[2]的基础上,把[5]中带算BCK—代数的概念加以抽象化,引进BE—代数上的模概念以及半本原BE—代数和BE—代数的Jacobson根,讨论这种模的一些基本性质,给出Jacobson根的表达式,证明了半本原BE—代数的结构定理。本文中BE—代数均指M(E):(E,·,1)为么半群。所用符号和术语同[1]、[2]、[3]、[4]。     

Isomorphism of extensions of C(T~2)

In this paper we give a certain classification theorem of extensions of the torus algebra up to isomorphism and also show that the K 0 -group K 0 (E) and the semigroup V (E) are two complete invariants of such extension algebras.     

Homomorphisms of weighted algebras of continuous functions

Summary A characterization is given of all continuous algebra homomorphisms H from the weighted space of continuous functions CV(X, E) into ℂ, where X is a completely regular Hausdorff space, E a locally convex algebra and V a family of weight functions that vanish at infinity. These homomorphisms are represented in the form H(f) = h(f(x)) with x in X and h a continuous algebra homomorphism on E. We then consider the space of homomorphisms of CV(X, E) and give some counterexamples to possible further generalizations. Entrata in Redazione il 18 febbraio 1977. ? Aspirant ? of the Belgian ? Nationaal Fonds voor Wetenschappelijk Onderzoek ?.     

Length two extensions of modules for the Witt algebra

In this paper, we establish an explicit classification of length two extensions of tensor modules for the Witt algebra using the cohomology of the Witt algebra with coe?cients in the module of the space of homomorphisms between the two modules of interest. To do this we extended our module to a module that has a compatible action of the commutative algebra of Laurent polynomials in one variable. In this setting, we are be able to directly compute all possible 1-cocycles.     

Algebra homomorphisms defined via convoluted semigroups and cosine functions

Transform methods are used to establish algebra homomorphisms related to convoluted semigroups and convoluted cosine functions. Such families are now basic in the study of the abstract Cauchy problem. The framework they provide is flexible enough to encompass most of the concepts used up to now to treat Cauchy problems of the first- and second-order in general Banach spaces. Starting with the study of the classical Laplace convolution and a cosine convolution, along with associated dual transforms, natural algebra homomorphisms are introduced which capture the convoluted semigroup and cosine function properties. These correspond to extensions of the Cauchy functional equation for semigroups and the abstract d'Alembert equation for the case of cosine operator functions. The algebra homomorphisms obtained provide a way to prove Hille-Yosida type generation theorems for the operator families under consideration.     

Some Problems on Homomorphisms and Real Function Algebras

 In this paper we solve a problem about the representation of all homomorphisms on a real function algebra as point evaluations and another two about function algebras in which homomorphisms are point evaluations on sequences in the algebra. (Received 4 December 2000; in revised form 2 April 2001)     

Homomorphisms of algebras

A construction of all homomorphisms of an algebra with a finite number of operations into an algebra of the same type is presented that consists in replacing algebras by suitable mono-unary algebras (possibly with some nullary operations) and their homomorphisms by suitable homomorphisms of the corresponding mono-unary algebras. Since a construction of all homomorphisms between two mono-unary algebras is known (see, e.g., [6], [7], [8]), a construction of all homomorphisms of an arbitrary algebra with a finite number of operations into an algebra of the same type can be described.     

AN EMBEDDING THEOREM BETWEEN SPECIAL LINEAR GROUPS OVER ANY FIELDS

ＡＮＥＭＢＥＤＤＩＮＧＴＨＥＯＲＥＭＢＥＴＷＥＥＮＳＰＥＣＩＡＬＬＩＮＥＡＲＧＲＯＵＰＳＯＶＥＲＡＮＹＦＩＥＬＤＳ￥ＺＨＡＪＩＡＮＧＵＯ（ＤｅｐａｒｔｍｅｌｌｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｏｎｇｊｉＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａ...     

Sums and extensions of vector lattice homomorphisms

This paper gives a summary account, with minimal or no proofs, first of some results which characterize order bounded linear operators which are sums of lattice homomorphisms, or more generally of orthomorphisms; and secondly of theorems concerning extensions of vector lattice homomorphisms (theorems of Hahn-Banach type if you will). In all cases we assume that domain and range are vector lattices and that the range is Dedekind complete. The results vary from historical (pre-1940) to recent (1990). The most recent work, on sums of lattice homomorphisms, is covered in §1 and the more classical work on extension theorems is dealt with in §2.     

Homomorphisms of heterogeneous algebras

A construction of all homomorphisms of a heterogeneous algebra into an algebra of the same type is presented. A relational structure is assigned to any heterogeneous algebra, and homomorphisms between these relational structures make it possible to construct homomorphisms between heterogeneous algebras. Homomorphisms of relational structures can be constructed using homomorphisms of algebras that are described in [11].     

Identities of representations of nilpotent lie algebras

Lret N be a nilpotent of class 2 Lie algebra with one-dimensional centre C = Kc over an infinite field K and let p : N → End_k:(V) be a representation of N in a vector space V such that p(c) is invertible in End_k(V). We find a basis for the identities of the representation p. As consequences we obtain a basis for all the weak polynomial identities of the pair (M₂:(K), s1₂(K)) over an infinite field K of characteristic 2 and describe the identities of the regular representation of Lie algebras related with the Weyl algebra and its tensor powers.