向量值Musielak-Orlicz空间的两种几何性质(英)

设Ｘ是复Ｂａｎｃｈ空间,Ｍ（ｔ,ｕ）是以ｔ为参数的满足某些通常条件的Φ－函数．我们证明了;（ｉ）Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ空间Ｌ_Ｍ（Ｘ）具有解析ＵＭＤ性质当且仅当Ｘ具有;（ｉｉ） Ｌ_Ｍ（Ｘ）具有解析ＲＮ性质当且仅当Ｘ具有．     

Orlicz序列空间的（弱）正规结构和（LD）性质

本文讨论赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间ＬＭ，主要结果如下：（１）ＬＭ具有Ｌａｍｉ－Ｄｏｚｏ性质     

L(φ,μ)-平均域及其几何特征

本文首先引入 Ｌ（φ,μ）－平均域,它是已知的 Ｊｏｈｎ－域, Ｌｓ－平均域和 Ｌｓ（μ）－平均域等的推广．然后利用拟双曲度量来刻画Ｌ（φ,μ）－平均域的几何特征．最后证明,对于任何满足Ｌ（φ,μ）－平均域定义中条件的函数φ, Ｊｏｈｎ－ 域是 Ｌ（φ,μ）－平均域．     

关于可分解算子的扰动的不变子空间(英文)

在文献［１］中,Ｊ．Ｅｓｃｈｍｅｉｅｒ和Ｂ．Ｐｒｕｎａｒｕ证明了（复）Ｂａｎａｃｈ空间上的每个具有Ｂｉｓｈｏｐ性质（β）和浓厚谱的有界线性算子有非平凡的不变子空间．在文献［２］中,Ｈ．Ｍｏｈｅｂｉ和Ｍ．Ｒａｄｊａｂａｌｉｐｏｕｒ在减弱算子的Ｂｉｓｈｏｐ性质（β）和加强谱的浓厚性条件的情况下得到了另外几个不变子空间定理．本文给出了一个更进一步的不变子空间定理（见定理１）．     

赋Orlicz范数的Musielak-Orlicz序列空间的单调点

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间中上（下）单调点以及上（下）局部一致单调点的充分必要条件．     

θ(t)-Caldern-Zygmund算子在群上的Hardy空间H~p(G)中的有界性

设Ｇ为局部域Ｋ上的２ｎ＋１维Ｈｅｉｓｅｎｂｅｒｇ群,文献［１］给出了一类Ｈａｒｄｙ空间 Ｈ~ｐ（Ｇ）,（０＜Ｐ≤１）,本文讨论了θ（ｔ）－Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ算子在Ｈ~ｐ（Ｇ）（０＜Ｐ≤１）中的有界性。     

赋Orlicz范数的Musielak-Orlicz空间的光滑点与强光滑点(英)

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ函数空间中光滑点、光滑性、强（很）光滑点和强（很）光滑性的充 分必要条件．     

关于L2空间中的Bernstein-MarkoV不等式

纠正了闵国华（１９９２年）关于Ｌ＾２空间中的Ｂｅｒｎｓｔｅｉｎ－Ｍａｒｋｏｖ不等式的几个错误结果。     

BLOCKBASISOFSEQUENCEORLICZSPACES

本文证明如果奥尔里奇函数Ｍ满Δ２条件并且ｌｉｍｉｎｆｂ→０ｌｉｍｓｕｐａ→０Ｍ（ａｂ）／Ｍ（ａ）Ｍ（ｂ）＝０或者ｌｉｍｓｕｐｂ→０ｌｉｍｉｎｆａ→０Ｍ（ａｂ）／Ｍ（ａ）Ｍ（ｂ）＝０那么奥尔里序列空间ｌＭ不同构于它的由标准基的块基（其系数趋向于零）张成的任何子空间     

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])．     

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.     

Strong duals of projective limits of (LB)-spaces

We investigate the problem when the strong dual of a projective limit of (LB)-spaces coincides with the inductive limit of the strong duals. It is well-known that the answer is affirmative for spectra of Banach spaces if the projective limit is a quasinormable Fréchet space. In that case, the spectrum satisfies a certain condition which is called strong P-type. We provide an example which shows that strong P-type in general does not imply that the strong dual of the projective limit is the inductive limit of the strong duals, but on the other hand we show that this is indeed true if one deals with projective spectra of retractive (LB)-spaces. Finally, we apply our results to a question of Grothendieck about biduals of (LF)-spaces.     

On the completion of (LF)-spaces

Once the existence of metrizable (LF)-spaces was discovered, the problem whether the completion of an (LF)-space is or is not an (LF)-space was answered in the negative, because no (LF)-space can be a Fréchet space. However, some (non-metrizable) (LF)-spaces are complete, e.g. the classical Köthe's strict (LF)-spaces. In this paper we will carry out a thorough study of the completeness of (LF)-spaces stressing upon the stable completion properties of (LB)-spaces. A basic tool for handling this problem is an Open Mapping Theorem for completions of (LF)-spaces, which is also proved in the present paper.This research, supported by a Fulbright-MEC fellowship, was carried out during the author's visit at the University of Maryland while on leave from the University of Extremadura. The author is grateful to Professor S. A. Saxon for very helpful conversation and, especially, for calling his attention to the problem of completions of (LF)-spaces.     

A characterization of weighted (<Emphasis Type="Italic">LB</Emphasis>)-spaces of holomorphic functions having the dual density condition

We characterize when weighted (LB)-spaces of holomorphic functions have the dual density condition, when the weights are radial and grow logarithmically.     

Well-ordered (F) spaces are D-spaces

We study the relationship between the Collins–Roscoe mechanism and D-spaces, and prove that well-ordered (F) spaces are D-spaces. This improves a previous result of D. Soukup and X. Yuming [17].     

Banach Spaces with Property (M) and their Szlenk Indices

We show that a separable Banach space with property (M*) has a Szlenk index equal to ω₀, and a norm with an optimal modulus of asymptotic uniform smoothness. From this we derive a condition on the Szlenk functions of the space and its dual which characterizes embeddability into c ₀ or an ℓ _p -sum of finite dimensional spaces. We also prove that two Lipschitz-isomorphic Orlicz sequence spaces contain the same ℓ _p -spaces.      

A(X,M)-c-内射性

本文研究了X-扩张模.利用A( X,M)-c-内射模的概念,获得了A( X,M)-c-内射模的有限直和仍是A( X,M)-c-内射模的一个充分必要条件,并推广了相应的结果.     

Fréchet-valued holomorphic functions on compact sets in (DFN)-spaces

We establish the equivalence between the weak holomorphicity and holomorphicity of Fréchet-valued functions on compact polydisks in (DFN)-spaces. Moreover, the relations between separately holomorphic functions and holomorphic functions on compact polydisks in (DFN)-spaces are also given. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1578–1584, November, 2008.