无界可分解算子的对偶定理

本文利用有界可分解算子对偶定理建立了文献[7]中引进的无界可分解算子的对偶定理,证明了,T是可分解算子且X_T({∞})={0}当且仅当T~*是可分解算子且X_((T~*))~*({∞})={0~*}。     

强可分解算子的一个性质及其对偶定理

<正> 本文讨论强可分解算子的一个性质,在此基础上,指出强可分解算子的对偶定理不成立。 一、主要定理 设X为复Banach空间,B(X)为X上有界线性算子的全体.用C表复平面.设T∈B(X)具有单值延拓性,对E C,令     

闭算子的谱对偶定理Ⅲ

本文讨论了闭算子的谱对偶定理,即证明了:对于定义在复Banach空间X内的稠定闭算子T,当T^*具有SDP时,T也具有SDP。     

无界S-可分解算子的对偶定理(Ⅱ)

关于无界可分解算子的对偶理论,国内外不少学者都在从事研究,但有的附加了若干条件才加以解决,有的则论证过程还存在一些问题.今年,王声望教授在文献[1]中不加任何条件彻底地解决了这个问题.本文试图在王声望工作的基础上,讨论无界S-可分解算子的对偶定理. 本文中,我们用C和C_∞分别表示复平面和扩充的复平面,用C(X)表示复Banach空间X     

可分解算子的谱容度

在本文里,我们引进封闭线性算子的谱容度概念, 我们证明T是封闭可分解算子当且仅当T具有谱容度。     

闭算子的谱对偶定理(Ⅱ)

本文研究具有谱分解性质的闭算子T的对偶定理。经过若干准备后,在T,T~*,T~(**)均为稠定的假定下,证明了当T~*具有SDP时,T也具有SDP,从而部分地回答了下述问题:当T~*具有SDP时,T是否也具有SDP?     

商不可分解Banach空间上线性算子的谱

This paper discusses the special properties of the spectrum of linear operators (in particular, bounded linear operators) on quotient indecomposable Banach spaces; shows that in such spaces generators of Co-groups are always bounded linear operators, and that generators of Co-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of Co-semigroups in quotient indecomposable spaces are not necessarily bounded.     

广义Sublaplace算子的谱乘子定理

本文通过建立与广义Ｓｕｂｌａｐｌａｃｅ算子Ｌ相关的Ｌｉｔｌｅｗｏｏｄ－Ｐａｌｅｙ理论，得到Ｌ的谱乘子定理，作为该结果的应用，并给出一类Ｌａｇｕｅｒｅ函数展开的乘子定理     

可分解算子的某些性质

In this paper, we have proved the following two theorems: Theorem1. If T⁽⁴⁾∈SVEP, then τX is an analytic invariant subspace of T⁽²⁾, where τ is the natural imbedding from X to X⁽²⁾.Theorem 2. If T⁽¹⁾ is decomposable, then T is decomposable too.The authois take this opportunity to express their gratitude to the author of [2].     

一类不可分解Banach空间上线性算子的谱性质

给出一类不可分解的∑_e~1型Banach空间上线性算子(不一定有界)的谱结构,并讨论这种空间上生成C_0群或C_0半群的线性算子的有界性、特殊的谱性质和谱结构,还给出这种空间上闭算子是有界算子的一个充分条件。     

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）．     

A Composition Theorem for Multiple Summing Operators

We prove that the composition S(u₁, …, u_n) of a multilinear multiple 2-summing operator S with 2-summing linear operators u_j is nuclear, generalizing a linear result of Grothendieck.     

A Composition Theorem for Multiple Summing Operators

We prove that the composition S(u₁, …, u_n) of a multilinear multiple 2-summing operator S with 2-summing linear operators u_j is nuclear, generalizing a linear result of Grothendieck. Both authors were partially supported by DGICYT grant BMF2001-1284.     

A Functional Limit Theorem for Decomposable Branching Processes with Two Particle Types

A decomposable Galton–Watson branching process with two particle types is studied. It is assumed that the particles of the first type produce equal numbers of particles of the first and second types, while the particles of the second type produce only particles of their own type. Under the condition that the total number of particles of the second type is greater than N →∞, a functional limit theorem for the process describing the number of particles of the first type in different generations is proved.     

A Note on Equivalent Theorem for Beta Operators

In this paper, we give an equivalent theorem concerning on the whole interval [0, +∞). Both the direct and converse theorems are derived. These results bridge the gap between the point-wise conclusions and global conclusions.     

A Generalization of De Vries Duality Theorem

Generalizing Duality Theorem of H. de Vries, we define a category which is dually equivalent to the category of locally compact Hausdorff spaces and perfect maps.     

A Global Inverse Theorem for Combinations of Phillips Operators

Mediterranean Journal of Mathematics - In the present paper, we prove a global inverse theorem for approximation of bounded continuous functions on the interval [0, ∞) by linear combinations...