(NCI)算子与(NFI)算子

引入两类与不变子空间密切相关的算子,即(NCI)算子与(NFI)算子.考虑这两类算子的性质,例如存在性,相似不变性,以及与强不可约算子的关系等.并在可分Banach空间上讨论谱为单点集{0}的算子能否小紧摄动成为(NFI)算子.     

本质正规算子的迹类算子扰动

本文利用ＢＤＦ定理以及构造技巧证明了关于本质正规算子的Ｐｅａｒｃｙ－Ｓａｌｉｎａｓ定理．作为此定理的应用，证明了本质正规算子可以通过迹类算子的小扰动成为不可约算子．     

Banach空间上的闭强不可约算子

本文首先给出Banach空间上闭强不可约算子的定义,并给出一个无界强不可约算子的例子;其次给出闭强不可约算子的性质,特别地,给出了闭强不可约算子的一些等价描述;最后给出上三角算子矩阵表示的闭算子具有强不可约性的一些充分条件.     

幂零算子相似于不可约算子

给出幂零算子相似于不可约算子的充要条件,并且对幂零算子证明了Herrero猜想.     

Hilbert空间有限强不可约分解算子

本文在Ｈｉｌｂｅｒｔ空间引入了有限强不可约分解算子及其强不可约分解在相似意义下的唯一性的概念,初步讨论了有限强不可约分解算子的性质,证明了一些算子的强不可约分解在相似意义下是唯一的．     

Bergman空间上一类解析Toeplitz算子的强不可约性

令D为单位圆盘D={z∈C:|z|<1},L_a~2(D)为L~2(D)中解析函数构成的Bergman空间.设f(z)=a_0+a_1z+a_2z~2+…,用算子理论的技巧给出解析Toeplitz算子T_f为强不可约算子的一个充分条件.     

紧扰动下的谱连通算子是强不可约的 *

回答了D .A .Herrero于1988年提出的一个猜测 :可分复Hilbert空间上每个谱连通算子在紧扰动下是强不可约的 .     

Cowen-Douglas算子的拟相似

证明了对任意T∈L (H), 如果T拟相似于强不可约Cowen-Douglas算子, 则T也是强不可约的. 回答了Davidson和Herrero提出的问题.     

自反Banach格上正算子基态的存在性

非负算子基态的存在性,是Perron-Frobenius型定理的核心内容,也是证明算子谱缝隙的主要步骤.本文主要利用了正算子非半紧测度的概念,讨论了一般自反Banach格上正算子基态的存在性,并得到了一个充分条件.更为特殊的,若算子同时满足不可约性,证明了基态特征向量是严格正的.     

复合算子和一类解析Toeplitz算子的约化子空间

本文利用复合算子完全刻画了符号为两个Ｂｌａｓｃｈｋｅ因子乘积的解析Ｔｏｅｐｌｉｔｚ算子的约化子空间。     

Quasitriangular + small compact = strongly irreducible

Let be a bounded linear operator acting on a separable infinite dimensional Hilbert space. Let be a positive number. In this article, we prove that the perturbation of by a compact operator with can be strongly irreducible if is a quasitriangular operator with the spectrum connected. The Main Theorem of this article nearly answers the question below posed by D. A. Herrero.

Suppose that is a bounded linear operator acting on a separable infinite dimensional Hilbert space with connected. Let be given. Is there a compact operator with such that is strongly irreducible?

     

Strongly Irreducible Submodules of Modules

Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N or K ∈ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R-module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.     

具有g个零强分支的有向图的传递指数

研究了传递矩阵的图论,及布尔矩阵幂的若干图论性质,给出了有向图(布尔矩阵)传递指数的上、下界估计,从而改进了已有的结果.     

Subdirectly irreducible \mathcal{RGC} -commutative right H-semigroups

A semigroup S is said to be ℛ-commutative if, for all elements a,b∈S, there is an element x∈S ¹ such that ab=bax. A semigroup S is called a generalized conditionally commutative (briefly, -commutative) semigroup if it satisfies the identity aba ²=a ² ba. An ℛ-commutative and -commutative semigroup is called an -commutative semigroup. A semigroup S is said to be a right H-semigroup if every right congruence of S is a congruence of S. In this paper we characterize the subdirectly irreducible semigroups in the class of -commutative right H-semigroups. Research supported by the Hungarian NFSR grant No T029525.     

Homomorphic images of finite subdirectly irreducible unary algebras

We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty. While working on this paper the first and the third authors were partially supported by the Grant Agency of the Czech Republic, grant #201/02/0594, and by the institutional grant MSM0021620839; the second author was supported by the Ministry of Science, Technologies and Development of Republic of Serbia, grant no. 1227.     

On fuzzy irreducible ideals and homomorphisms

The algebraic nature of fuzzy irreducible ideals under homomorphisms is discussed.     

Algorithms for finding proper essential surfaces in 3-manifolds

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold.     

On completely irreducible operators

Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more. The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section 2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties of completely irreducible operators are different from properties of unicellular operators. __________ Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29     

整系数多项式在整数环上不可约性的进一步探讨

本文首先给出了整系数多项式有二次整系数多项式因式的一个必要条件，进而通过对整系数多项式ｆ（ｘ）＝ＡｎＸ２十αｎ－１Ｘｎ－１＋…＋αｏ中ｘｎ－２的系数αｎ－２的讨论，得到一类整系数多项式在整数环上是否可约的一个判别法。     

投入产出分析中完全消耗系数矩阵的性质

本文讨论了投入产出分析中,当某一消耗系数变化时,完全消耗系数矩阵变化的特点,并研究了当最终需求不变时,直接消耗系数的变化对固定折旧、社会纯收入和劳动报酬的影响。