算子值加权模式在Banach空间的实现理论

本文处理能在Ｂａｎａｃｈ空间中实现的线性连续时间系统．这里，输入、输出和状态空间都是无穷维Ｂａｎａｃｈ空间．我们证明：加权模式有Ｂａｎａｃｈ空间实现的充要条件是它强连续且为指数阶．对状态算子是解析半群的无穷小生成元的情况，得到了Ｂａｎａｃｈ空间实现的存在性定理．所有定理都是在时间域中给出的．     

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。     

关于有界线性算子的可凹性及其Radon-Nikodym性质

本文运用向量测度方法研究了Ｂａｎａｃｈ空问上可凹算子类与Ｒａｄｏｎ－Ｎｉｋｏｄｙｍ算子类的特性,并把所得结果用于研究Ｂａｎａｃｈ空间的结构,给出Ｂａｎａｃｈ空间具有Ｒａｎｄｏｎ－Ｎｉｋｏｄｙｍ性质的若干新特征。     

一类解析算子函数空间上的复合算子

本文用算子函数论的方法，研究了解析算子函数的Banach空间X，X0上的复合算子．给出此复合算子为有界的条件，并刻划了此复合算子在X0上为紧的特征．     

Ｐ型基和良性有界算子

在自反Ｂａｎａｃｈ空间上一个有界线性算子是（Ｂ）型良性有界的当且仅当它的共扼算子也是（Ｂ）型的。但在非自反Ｂａｎａｃｈ空间上这种性质不成立。本文证明在一大类非自反Ｂａｎａｃｈ空间上总存在一个（Ｂ）型良性有界线性算子，它的共扼算子不是（Ｂ）型的。同时也证明了在具有基的Ｂａｎａｃｈ空间上，任何Ｐ型基序列一定有一个子序弄能够扩张成该空间的一个基。     

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。     

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...     

Harby空间上的复合算子

本文讨论n维复单位球的Harby空间上的复合算子，主要是利用Banach代数和n维单位球上解析函数的理论，给出了这类空间上复合算子的一个特征，证明了复合算子可逆的充要条件是其符号函数属于单位球的自同构群，并且对复合算子的范数作出了估计。     

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．     

非线性压缩算子半群的不变流

本文主要给出了Ｂａｎａｃｈ空间中非线性压缩算子半群存在不交流的充要条件，并且在Ｃ＊－代数及Ｈｉｌｂｅｒｔ空间中刻划了正非线性压缩算子半群的特征．     

Composition operators acting on holomorphic Sobolev spaces

We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.

     

Composition operators on a Banach space of analytic functions

In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL _α ¹ (D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range. Supported by NNSFC No.19671036     

A new class of operators and a description of adjoints of composition operators

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple-valued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.     

Compact composition operators on weighted Hilbert spaces of analytic functions

We characterize the compactness of composition operators acting on a large family of Hilbert spaces of analytic functions which lie between Bergman and Dirichlet spaces. Our characterization is given in terms of generalized Nevanlinna counting functions.     

从β0到E(p,q)和E0(p,q)空间的复合算子

设ψ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子Cψ:Cψ(f)=foψ.我们利用从β0到E(p,q)和E0(p,q)空间的复合算子研究了空间E(p,q)和E0(p,q),给出了-个新的特征.     

Resolvent estimates and decomposable extensions of generalized Cesàro operators

We determine the spectrum of generalized Cesàro operators with essentially rational symbols acting on various spaces of analytic functions, including Hardy spaces, weighted Bergman and Dirichlet spaces. Then we show that in all cases these operators are subdecomposable.     

从α-Bloch空间到QK型空间的复合算子

Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator C_φ: C_φf = fοφ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into Q_K(p,q) and Q_(K,O)(p,q) spaces are discussed, where O < α < ∞.     

A_α~2上复合算子的Hilbert-Schmidt差分

本文设A_α~2为定义在n维复空间单位多圆柱上的加权Bergman空间,L为Bergman空间上有界复合算子的全体并赋予算子范数拓扑,应用复合算子的HilbertSchmidt差分研究L的拓扑连通性.     

多圆柱上Bloch型空间之间的等距复合算子

简单介绍了一些解析函数构成的Banach空间上的满等距的结果,然后刻画了多圆柱上α-Bloch空间复合算子的等距,并得到了复合算子等距的充要条件.