Remarks on regular (LF)-spaces

Developing ideas found in a recent paper of Gilsdorf to arbitrary topological vector spaces (tvs) one shows that a Hausdorff (LB) _tv -spaceE is regular provided every null-sequence inE has a series convergent subsequence inE. Received by the editors 1980Mathematics Subject Classification (1985 Revision) 46A12.     

Sequential Completeness of LF-Spaces

Any LF-space is sequentially complete iff it is regular.     

弱序列式回缩(LM)-空间的特征

本文研究Retakh's条件(M_0),正则性和弱序列式回缩性之间的关系．对于(LM)-空间,弱序列式回缩性等价于正则性加上一个介于(Q_0)和(M_0)之间的条件对于(LN)-空间,我们获得了更满意的结果,证明了弱序列式回缩性等价于正则性加上条件(M_0),也等价于一个非常弱的正则性条件加上条件(M_0)(见文献[1-28])．     

On bornologicalC $$\overline V $$ (X) spaces

Archiv der Mathematik -     

Sequentially Complete Inductive Limits and Regularity

A notion of an almost regular inductive limits is introduced. Every sequentially complete inductive limit of arbitrary locally convex spaces is almost regular.     

拟速完备性与网状空间的诱导极限

设（Ｅ，ζ）＝ｉｎｄｌｉｍ（Ｅ_n，ζ_n）为局部凸空间的诱导极限．称（ＤＳＴ）成立若（Ｅ，ζ）中每个有界集含于且有界于某（Ｅ_n，ζ_n）．引进一种弱于速完备性的性质，叫做拟速完备性，并证明了对于严格网状空间的诱导极限，拟速完备性蕴涵（ＤＳＴ）．利用ＤｅＷｉｌｄｅ的理论，也给出了关于（ＤＳＴ）的其他条件．这些结果改进了已有的有关结论     

Topological entropy, embeddings and unitaries in nuclear quasidiagonal -algebras

Using topological entropy of automorphisms of -algebras, it is shown that some important facts from the theory of AF algebras do not carry over to the class of algebras.

It is shown that in general one cannot perturb a basic building block into a larger one which almost contains it. The same entropy obstruction used to prove this fact also provides a new obstruction to the known fact that two injective homomorphisms from a building block into an algebra need not differ by an (inner) automorphism when they agree on K-theory.

     

Reflexive Property of Rings

Mason introduced the reflexive property for ideals, and then this concept was generalized by Kim and Baik, defining idempotent reflexive right ideals and rings. In this article, we characterize aspects of the reflexive and one-sided idempotent reflexive properties, showing that the concept of idempotent reflexive ring is not left-right symmetric. It is proved that a (right idempotent) reflexive ring which is not semiprime (resp., reflexive), can always be constructed from any semiprime (resp., reflexive) ring. It is also proved that the reflexive condition is Morita invariant and that the right quotient ring of a reflexive ring is reflexive. It is shown that both the polynomial ring and the power series ring over a reflexive ring are idempotent reflexive. We obtain additionally that the semiprimeness, reflexive property and one-sided idempotent reflexive property of a ring coincide for right principally quasi-Baer rings.     

Banach Lattices on Which Every Power-Bounded Operator is Mean Ergodic

Given a Banach lattice E that fails to be countably order complete, we construct a positive compact operator A: E E for which T = I - A is power-bounded and not mean ergodic. As a consequence, by using the theorem of R. Zaharopol, we obtain that if every power-bounded operator in a Banach lattice is mean ergodic then the Banach lattice is reflexive.     

Retakh条件(M0)与弱(序列式)紧正则性

本文研究了弱(序列式)紧正则诱导极限与凸弱(序列式)紧正则诱导极限.满足Retakh条件(Mo)的(LF)-空间必为凸弱(序列式)紧正则的,但未必为弱(序列式)紧正则的.对于弱序列式完备Frechet空间的可数诱导极限,Retakh条件(Mo)蕴涵弱(序列式)紧正则性.特别地,对于Kothe(LF)-序列空间Ep(1≤p<∞),Retakh条件(Mo)等价于弱(序列式)紧正则性.对于这类空间,利用Vogt的有关结论,给出了弱(序列式)紧正则性的特征.     

诱导极限中的弱紧集

本文研究了诱导极限中的弱集与紧集，我们给出了诱导极限ｉｎｄｉｍ Ｅｎ中每个弱紧集含于且弱紧于某Ｅｎ的一些条件。     

Reflexive rings and their extensions

A right ideal I is reflexive if xRy ∈ I implies yRx ∈ I for x, y ∈ R. We shall call a ring R a reflexive ring if aRb = 0 implies bRa = 0 for a, b ∈ R. We study the properties of reflexive rings and related concepts. We first consider basic extensions of reflexive rings. For a reduced iedal I of a ring R, if R/I is reflexive, we show that R is reflexive. We next discuss the reflexivity of some kinds of polynomial rings. For a quasi-Armendariz ring R, it is proved that R is reflexive if and only if R[x] is reflexive if and only if R[x; x ^?1] is reflexive. For a right Ore ring R with Q its classical right quotient ring, we show that if R is a reflexive ring then Q is also reflexive. Moreover, we characterize weakly reflexive rings which is a weak form of reflexive rings and investigate its properties. Examples are given to show that weakly reflexive rings need not be semicommutative. It is shown that if R is a semicommutative ring, then R[x] is weakly reflexive.     

图象的自反与渐近自反

本文对B（X,Y）的自反子空间及渐近自反子空间上的映射（或映射组）,分别给出了一些判别它们的图象（或联合图象）仍为自反及渐近自反的方法。     

Toeplitz operators on the space of analytic functions with logarithmic growth

Continuous and compact Toeplitz operators for positive symbols are characterized on the space of analytic functions with logarithmic growth on the open unit disc of the complex plane. The characterizations are in terms of the behaviour of the Berezin transform of the symbol. The space was introduced and studied by Taskinen. The Bergman projection is continuous on this space in a natural way, which permits to define Toeplitz operators. Sufficient conditions for general symbols are also presented.     

矩阵方程组$AX=B,XC=D$的Hermitian自反(反Hermitian自反)最小二乘解及其最佳逼近

In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.     

一类Riccati矩阵方程广义自反解的双迭代算法

本文研究了一类Riccati矩阵方程广义自反解的数值计算问题.利用牛顿算法将Riccati矩阵方程的广义自反解问题转化为线性矩阵方程的广义自反解或者广义自反最小二乘解问题,再利用修正共轭梯度法计算后一问题,获得了求Riccati矩阵方程的广义自反解的双迭代算法.拓宽了求解非线性矩阵方程的迭代算法.数值算例表明双迭代算法是有效的.     

Retakh条件(M0)与弱(序列式)紧正则性

本文研究了弱（序列式）紧正则诱导极限与凸弱（序列式）紧正则诱导极限.满足Retakh条件（M₀）的（LF）-空间必为凸弱（序列式）紧正则的,但未必为弱（序列式）紧正则的.对于弱序列式完备Frechet空间的可数诱导极限,Retakh条件（M₀）蕴涵弱（序列式）紧正则性.特别地,对于Kothe（LF）-序列空间Ep（1≤p<∞）,Retakh条件（M₀）等价于弱（序列式）紧正则性.对于这类空间,利用Vogt的有关结论,给出了弱（序列式）紧正则性的特征.     

Strong Reflexivity of Abelian Groups

A reflexive topological group G is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group G and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.