Banach空间有界线性算子强连续双半群

本文在Ｂａｎａｃｈ空间上研究单参数有界线性算子族－强连续双半群。     

B（X）上的保k次幂线映射

设Ｘ为Ｂａｎａｃｈ空间,Ｂ（Ｘ）为ＺＨ 有界线性算子全体组成的代数,本文给出了Ｂ（Ｘ）上保ｋ次幂弱连续线性满足射的完全刻划。     

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）．     

Banach空间双曲型算子方程的解

Ｂａｎａｃｈ空间双曲型算子方程的解杨根科，卫淑芝（太原重型机械学院数学教研室，太原０３００２４）§１．引言考虑Ｂａｎａｃｈ空间Ｅ中双曲型算子方程解的存在性；这里，是（Ｃ０）类线性算子半群的无穷小生成元。本文研究（１）整体温和解的存在性，解决了一类常规...     

Banach空间中一类度量投影的判据及表达式

X为自反、严格凸Ｂａｎａｃｈ 空间,L为X中闭子空间,P：X→L为单值算子,该文给出P成为L上度量投影P_L的判据及P_L为线性算子的充分必要条件．在自反Ｂａｎａｃｈ空间中,利用对偶映射,给出超平面上（值）度量投影的表达式．对于自反、严格凸、光滑的Ｂａｎａｃｈ 空间中线性流形上的（单值）度量投影,利用广义右逆的表示,求出其表达式．在后继文章中将给出此表达式的应用．     

关于余弦算子函数的一个结果

设Ａ是Ｂａｎａｃｈ空间Ｘ中的闭线性算子,对凡　是单射。文中定义了Ｂａｎａｃｈ空间　范数　强于Ｘ的范数。我们证明了算子Ａ在空间Ｚ中的部分ＡＺ生成Ｚ中的一个余弦算子函数,空间Ｚ具有某种意义上的极大性。     

B(X)上的保k次幂线性映射

设Ｘ 为Ｂａｎａｃｈ 空间,Ｂ（Ｘ）为Ｘ 上有界线性算子全体组成的代数,本文给出了Ｂ（Ｘ）上保ｋ 次幂弱连续线性满射的完全刻划．     

Banach格上正则算子格

本文首先对 Ｂａｎａｃｈ格 Ｅ给出了条件,使得对任意非 Ｄｅｄｅｋｉｎｄ　σ－完备的Ｂａｎａｃｈ格Ｆ,正则算子空间Ｌ~ｒ（Ｅ,Ｆ）均是一Ｒｉｅｓｚ空间．其次对Ｂａｎａｃｈ格Ｆ给出了一些刻划,使之每个由Ｌ_ｐ－空间到Ｆ内的连续线性算子均是正则的．一些相关结果也得以讨论．     

非自反Banach空间无界控制算子的容许性

本文利用共轭Ｃ_０半群的扰动理论研究了无界容许控制算子，在太阳自反和非太阳自反Ｂａｎａｃｈ空间分别导出了一些容许性判据，并把这些抽象结果应用到了有限和无限延滞方程．     

关于强连续算子半群本质谱半径扰动的一个结果

设Ｂ是Ｂａｎａｃｈ空间Ｅ上强连续算子半群Ｔ０（ｔ）的无穷小生成母元，｜｜Ｔ０（ｔ）｜｜≤Ｍｅ￣（ｗｔ），Ｋ是Ｅ上的有界线性算子，本文证明了当Ｂ、Ｋ满足一定条件时，由Ｂ＋Ｋ生成的强连续半群Ｔ（ｔ）的本质谱半径ｒｅｓｓＴ（ｔ）≤ｅ￣（ｗｔ）     

Well-bounded operators on nonreflexive Banach spaces

Every well-bounded operator on a reflexive Banach space is of type (B), and hence has a nice integral representation with respect to a spectral family of projections. A longstanding open question in the theory of well-bounded operators is whether there are any nonreflexive Banach spaces with this property. In this paper we extend the known results to show that on a very large class of nonreflexive spaces, one can always find a well-bounded operator which is not of type (B). We also prove that on any Banach space, compact well-bounded operators have a simple representation as a combination of disjoint projections.

     

Well-Boundedness of Sums and Products of Operators

A sufficient condition is given under which the sum, productand indeed any polynomial combination of a well-bounded operatorand a commuting real scalar-type spectral operator is well-bounded.This generalizes a result of Gillespie for Hilbert space operators.It is shown in particular that if X is a UMD space, then thesum of finitely many commuting real scalar-type spectral operatorsacting on X is a well-bounded operator (a result which failson general reflexive Banach spaces).     

关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

Minimal convex functions bounded below by the duality product

It is well known that the Fitzpatrick function of a maximal monotone operator is minimal in the class of convex functions bounded below by the duality product. Our main result establishes that, in the setting of reflexive Banach spaces, the converse also holds; that is, every such minimal function is the Fitzpatrick function of some maximal monotone operator. Whether this converse also holds in a nonreflexive Banach space remains an open problem.

     

James' Theorem Fails for Starlike Bodies

Starlike bodies are interesting in nonlinear functional analysis because they are strongly related to bump functions and to n-homogeneous polynomials on Banach spaces, and their geometrical properties are thus worth studying. In this paper we deal with the question whether James' theorem on the characterization of reflexivity holds for (smooth) starlike bodies, and we establish that a feeble form of this result is trivially true for starlike bodies in nonreflexive Banach spaces, but a reasonable strong version of James' theorem for starlike bodies is never true, even in the smooth case. We also study the related question as to how large the set of gradients of a bump function can be, and among other results we obtain the following new characterization of smoothness in Banach spaces: a Banach space X has a C¹ Lipschitz bump function if and only if there exists another C¹ smooth Lipschitz bump function whose set of gradients contains the unit ball of the dual space X*. This result might also be relevant to the problem of finding an Asplund space with no smooth bump functions.     

On a problem of Namioka on norm-attaining functionals

Isaac Namioka conjectured that every nonreflexive Banach space can be renormed is such a way that, in the new norm, the set of norm attaining functionals has an empty interior in the norm topology. We prove the rightness of this conjecture for spaces containing an isomorphic copy of ℓ₁. As a consequence, we prove also that the same result holds for a wide class of Banach spaces containing, for example, the weakly compactly generated ones.     

Compact adjoint operators and approximation properties

This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties.     

A Characterization of Schauder Frames Which Are Near-Schauder Bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of c ₀. In particular, a Schauder frame of a Banach space with no copy of c ₀ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of c ₀. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.     

Convergence Theorems for Best Approximations in a Nonreflexive Banach Space

In this paper, we study continuity properties of the mappingP: (x, A)→P_A(x) in a nonreflexive Banach space where PA is the metric projection onto A. Our results extend the existing convergence theorems on the best approximations in a reflexive Banach space to nonreflexive Banach spaces by using Wijsman convergence of sets.     

Variational-type inequalities for (η, θ, δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces

In this paper, we introduce (η, θ, δ)-pseudomonotone-type set-valued mappings and consider the existence of solutions to variational-type inequality problems for (η, θ, δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces.