Ⅱ1空间上JC*-代数的不变子空间

讨论了Ⅱ1空间上一般JC*-代数的不变子空间的存在条件问题,得到各类JC*-代数存在Ⅱ2型不变子空间的等价条件.     

∏1空间上JC*-代数的若干性质

在∏1空间上讨论了JC*-代数及其商代数的C*-等价性,理想的对称性,不变子空间的存在性以及交换性条件等问题,得到了若干结论.     

Pontrjagin空间上算子代数理想的对称性

本文证明了非退化的JC*-代数和非退化的JVN-代数的理想必是对称的.对退化的JC*-代数给出两种对称的理想和两种非对称的理想,说明了π1空间上JVN-代数除了第三类代数外无非对称理想,还构造两个关于JC*-代数理想对称性的例子.     

C*-代数中的不变子空间问题

本文获得了下述结果设A是一可分的单C*-代数,对每个a(≠0)∈A,则都存在可分的忠实不可约*表示(π,Hπ),使得π(a)在Hπ中具有非平凡不变子空间.该结果完全解决了HuaxinLin[1]所提问题.     

C~*-代数中的不变子空间问题

本文获得了下述结果：设 Ａ是一可分的单 Ｃ*-代数,对每个 ａ（≠０） ∈Ａ,则都存在可分的忠实不可约*表示（π,Ｈπ）,使得π（ａ）在 Ｈπ中具有非平凡不变子空间．该结果完全解决了 ＨｕａｘｉｎＬｉｎ［１］所提问题．     

Pontriagin空间上算子的交换性

证明了:当Pontrjagin空间上的正规算子A没有零性不变子空间时,Putnam- Fuglede定理成立;当正规算子A有零性不变子空问时,通过构造反例说明此时Putnam- Fuglede定理不成立,并对Π1空间上算子相关的交换性条件进行了讨论,得到了Π1空间上算子代数的二次交换定理．     

复平面上解析Banach空间的拟不变子空间

讨论复平面上解析Banach空间具有任意指标的拟不变子空间的存在性问题.首先给出一类复平面上解析Banach空间存在任意指标拟不变子空间的判定定理.作为应用,证明了Fock型空间F~p(C)={f∈Hol(C):1/π∫_C|f(z)|~pe~(-|z|~2)dA(z)+∞,1≤p+∞}与Hilbert空间H={f∈Hol(C):1/π∫_C|f(z)|~2e~(-|z|)dA(z)+∞}具有任意指标的拟不变子空间.     

Pontrjagin空间上一般算子代数弱闭和一致闭的等价条件

本文研究Pontrjagin空间上一般算子代数弱闭和一致闭的等价条件,得到定理:设C0(U),C1(U,L,R,D,V),C2a(U),C2b(U,R),C3a(U),C3b(U,R)分别是Ⅱk空间上第0,Ⅰ,Ⅱa,Ⅱb,Ⅲa和Ⅲb类的算子代数,则(1)C0(U),C2a(U)或C3a(U)为一致闭(弱闭)的等价条件是U是Hibert空间G上的C*-代数(W*-代数;(2)C1(U,L,R,D,V)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间,V是闭算子,L对称闭的;(3)C2b(U,R)或C3b(U,R)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间．     

套子代数上线性映射的Lie不变子空间

本文引入了Banach代数上线性映射的Lie不变子空间,给出了因子VonNeumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一般形式,研究了Lie导子与Lie自同构的概念及了Lie导子与Lie自同构半群的关系.     

不定度规空间上的K拟三角算子

在本文中,我们引入了Krein空间上K拟三角算子的概念,讨论了这类算子的一些代数性质,并在适当的条件下,证明了这类算子在其极大半定不变子空间上的限制存在非平凡的不变子空间。     

Unitarily-invariant linear spaces in C*-algebras

Characterisations and containment results are given for linear subspaces of a unital C*-algebra that are invariant under conjugation by sets of unitary elements of the algebra. The (unitarily-invariant) linear span of the projections in a simple, unital C*-algebra having non-scalar projections is shown to contain all additive commutators of the algebra and, in certain cases, to be equal to the algebra.

     

INVARIANT SUBSPACES AND EIGEVALUES OF ELEMENTS IN C-ALGEBRAS

Let A be a C~*-algebra and x an element in A. the following invariant subspace problem is considered: Does there exist an irreducible representation π of A such that π(x) has a non-trivial invarint subspace? And a positive solution of the problem for finite separable matroid C~*-algebras is given. Also the eigenvalues Of elements in C~*-algebras is considered. Some versions of Fredholm Alternatives are given.     

Partial Decidable Presentations in Hyperarithmetic

Siberian Mathematical Journal - We study the problem of the existence of decidable and positive $$\Pi_1^1$$ - and $$\Sigma_1^1$$ -numberings of the families of $$\Pi_1^1$$ - and $$\Sigma_1^1$$...     

Π_1空间上J-正常算子的J-酉等价

对于Π_1空间上J-正常算子的J-酉等价问题进行讨论.针对不同情况,给出了Π_1空间上两个J-正常算子J-酉等价的充要条件.这将有助于研究Π_1空间上交换J-von Neumann代数之间的J-酉等价.     

Representable Linear Functionals on Partial *-Algebras

A GNS-like *-representation of a partial *-algebra \mathfrak A{{\mathfrak A}} defined by certain representable linear functionals on \mathfrak A{{\mathfrak A}} is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.     

L 1 factorizations and invariant subspaces for weighted composition operators

For a contraction operator T with spectral radius less than one on a Banach space , it is shown that the factorization of certain L¹ functions by vectors x in and x*. in , in the sense that for n ≧ 0, implies the existence of invariant subspaces for T. Explicit formulae for such factorizations are given in the case of weighted composition operators on reproducing kernel Hilbert spaces. An interpolation result of McPhail is applied to show how this can be used to construct invariant subspaces of hyperbolic weighted composition operators on H². Received: 1 November 2005     

Hopf *-algebra structures on H(1, q)

We study the Hopf *-algebra structures on the Hopf algebra H(1, q) over ?. It is shown that H(1, q) is a Hopf *-algebra if and only if |q| = 1 or q is a real number. Then the Hopf *-algebra structures on H(1, q) are classified up to the equivalence of Hopf *-algebra structures.     

Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras

It is known that, under certain conditions, *-representability and extensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit, are equivalent. In this paper, a new condition for an analogous result is given for the case of a hermitian linear functional defined on a quasi *-algebra ${(\mathfrak{A}, \mathfrak{A}_0)}$ without unit.     

Closed Tripotents and Weak Compactness in the Dual Space of a Jb*-Triple

We revise the concept of compact tripotent in the bidual spaceof a JB*-triple. This concept was introduced by Edwards andRüttimann generalizing the ideas developed by Akemann forcompact projections in the bidual of a C*-algebra. We also obtainsome characterizations of weak compactness in the dual spaceof a JC*-triple, showing that a bounded subset in the dual spaceof a JC*-triple is relatively weakly compact if and only ifits restriction to any abelian maximal subtriple C is relativelyweakly compact in the dual of C. This generalizes a very usefulresult by Pfitzner in the setting of C*-algebras. As a consequencewe obtain a Dieudonné theorem for JC*-triples which generalizesthe one obtained by Brooks, Saitô and Wright for C*-algebras.     

IDEAL STRUCTURE IN CENTAIN C^*-TENSOR PRODUCTS

This paper discusses the ideal structure in tensor product $A\bigotimes B$ of C^*-algebra A and B,and introduces the concept of property (I) and property (K) with respect to the problem.When A is an AF(or scattered) C^*-algebra,it is shown that for any C^*-algebra B,the ideals in $A\bigotimes B$ can be expressed by those of A and B.