算子的拟酉等价性

本文在复的，可析的、无限维Ｈｉｂｅｒｔ空间Ｈ中引进了算子拟酉等价性的概念；获得了几个重要结果。     

本质正规算子模C2近似酉等价

本文刻划了本质正规算子模Ｃ２的近似酉等价，并且改进了Ｃａｒｒｙ和Ｐｉｎｃｕｓ在［１］中的一些结果。     

本质正规算子的模C_2近似酉等价

本文刻划了本质正规算子模的近似酉等价，并且改进了Ｃａｒｒｙ和Ｐｉｎｃｕｓ在［１］中的一些结果。     

Dirichlet空间上一类乘法算子的酉等价类

本文研究了Dirichlet空间D上由二阶Blaschke积φ定义的乘法算子M_φ的酉等价类.主要结果表明对于D的一个乘子ψ,乘法算子M_ψ酉等价于M_φ当且仅当存在常数θ,|θ|θ=1,使得ψ(z)=φ(θz).这一结果是完全不同于Hardy空间与Bergman空间上的相应结果.     

加权解析Lipschitz空间的等价范数

该文研究单位圆盘上加权解析Lipschitz空间的等价范数。作者首先推广文献［3］中的结果，给出了加权解析Lipschitz函数的p Garsia模刻画，然后用高阶导数刻画了加权解 析Lipschitz函数，并给出了它的Bergman Carleson测度特征。最后，还得到了加权解析Lipschitz函数类似于BMO指数衰减的John Nirenberg定理。     

闭子模的酉等价与遗传C*-子代数的稳定同构问题

在Hilbert C~*-模框架下,给出了闭子模之间的酉等价与相应的遗传C~*-子代数的*同构,及对应的开投影的等价性的关系定理.     

H~2(S_n)的不变子空间的酉等价

本文给出了Ｈ２（Ｓｎ）的两个不变子空间酉等价的必要条件．并证明了Ｈ２（Ｓｎ）的任何两个不变子空间经某种扩张后仅相差一个幺模函数．还讨论了Ｈ２（Ｓｎ）的两个不变子空间相差一个内函数因子的条件．     

Chaotic Unilateral Weighted Backward Shifts on Sequentially Complete Topological Sequence Spaces

Extending previous results of Grosse-Erdmann and Peris we obtain a characterization of chaotic unilateral weighted backward shifts on sequentially complete topological sequence spaces in which the canonical unit vectors(e_n)_n=1~∞ form an unconditional basis.     

Unitary Equivalence of Composition C$$^*$$-Algebras on the Hardy and Weighted Bergman Spaces

Let \(\varphi \) be an arbitrary linear-fractional self-map of the unit disk \({\mathbb {D}}\) and consider the composition operator \(C_{-1, \varphi }\) and the Toeplitz operator \(T_{-1,z}\) on the Hardy space \(H^2\) and the corresponding operators \(C_{\alpha , \varphi }\) and \(T_{\alpha , z}\) on the weighted Bergman spaces \(A^2_{\alpha }\) for \(\alpha >-1\). We prove that the unital C\(^*\)-algebra \(C^*(T_{\alpha , z}, C_{\alpha , \varphi })\) generated by \(T_{\alpha , z}\) and \(C_{\alpha , \varphi }\) is unitarily equivalent to \(C^*(T_{-1, z}, C_{-1, \varphi }),\) which extends a known result for automorphism-induced composition operators. For maps \(\varphi \) that are not automorphisms of \({\mathbb {D}}\), we show that \(C^*(C_{\alpha , \varphi }, {\mathcal {K}}_{\alpha })\) is unitarily equivalent to \(C^*(C_{-1, \varphi }, {\mathcal {K}}_{-1})\), where \({\mathcal {K}}_{\alpha }\) and \({\mathcal {K}}_{-1}\) denote the ideals of compact operators on \(A^2_{\alpha }\) and \(H^2\), respectively, and apply existing structure theorems for \(C^*(C_{-1, \varphi }, {\mathcal {K}}_{-1})/{\mathcal {K}}_{-1}\) to describe the structure of \(C^*(C_{\alpha , \varphi }, {\mathcal {K}}_{\alpha })/\mathcal {K_{\alpha }}\), up to isomorphism. We also establish a unitary equivalence between related weighted composition operators induced by maps \(\varphi \) that fix a point on the unit circle.     

Some Notes on M-hyponormal Weighted Shifts and Hyponormalizable Weighted Shifts

Let {an}∞n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main results are Theorems 4.1 and Theorems4.2. Theorem 4.1 gives the sufficient condition that a weighted shifts M-hyponormal operator is hyponormalizable. Theorem 4.2 gives the sufficient condition that a hyponormalizable weighted shift operator is M-hyponormal. Finally, invariant subspaces of such operators are discussed.     

Unitary Perturbations of Compressed n-Dimensional Shifts

Given any contractive matrix-valued analytic function ${\Theta}$ on the unit disc ${\mathbb{D}}$ , we construct a ${\mathcal{U}(n)}$ -parameter family of unitary operators which correspond to ${\Theta}$ in a natural way. These operators are unitarily equivalent to higher dimensional analogues of Clark’s unitary perturbations, a family of unitary operators associated to any self-map of the unit disc. Clark’s unitary perturbations were introduced in a seminal paper of Clark which has inspired the study of what are now called Aleksandrov–Clark measures. Our higher dimensional analogues of Clark’s unitary perturbations are applied to obtain matrix-generalizations of several classical results on the Aleksandrov–Clark measures associated to any holomorphic self-map of the unit disc. In particular we establish a matrix-valued Aleksandrov disintegration theorem for the Aleksandrov–Clark measures associated with matrix-valued contractive analytic functions ${\Theta}$ , and, by following results of Clark and Fricain in the scalar case, we provide a necessary and sufficient condition for the de Branges–Rovnyak space associated with ${\Theta}$ to contain a total orthogonal set of point evaluation vectors.     

Reflexivity of Weighted Shifts

Let {β（n）}n be a sequence of positive numbers such that β（0） = 1 and let 1 ≤ p 〈 ≤. We will investigate the reflexivity of all integer powers of the multiplication operator on the Banach spaces of formal Laurent series, L^P（β）.     

Disjoint Supercyclic Weighted Shifts

Complementing the existing literature in d-hypercyclicity, we characterize disjoint supercyclicity for a finite family of weighted shift operators. Using this characterization, we answer Question 2 in a recent paper by Bès, Martin and Peris in the negative by constructing examples of disjoint supercyclic weighted shifts whose direct sum operator is hypercyclic, but the same shifts operators fail to be disjoint hypercyclic. We also show the Disjoint Blow-Up/Collapse Property and the Strong Disjoint Blow-Up/Collapse Property for disjoint supercyclicity are equivalent when dealing with a finite family with two or more weighted shifts. However, those weighted shifts operators will never satisfy the Disjoint Supercyclicity Criterion. This provides a sharp distinction between disjoint supercyclicity and supercyclicity for a single operator. We provide a partial answer to disjoint supercyclic version of Question 3 in a recent paper by Salas by showing that we can always select an additional operator to add to an family of d-supercyclic weighted shift operators while maintaining the d-supercyclicity. We also show that, in general, this additional operator cannot be another weighted shift.     

On Unitary Equivalence of Analytic Toeplitz Operators

ＯｎＵｎｉｔａｒｙＥｑｕｉｖａｌｅｎｃｅｏｆＡｎａｌｙｔｉｃＴｏｅｐｌｉｔｚＯｐｅｒａｔｏｒｓＤｉｎｇＸｕａｎｈａｏ（丁宣浩）（ＤａｘｉａｎＴｅａｃｈｅｒ＇ｓＣｏｌｅｇｅ，Ｄａｘｉａｎ，Ｓｉｃｈｕａｎ，６３５０００）ＡｂｓｔｒａｃｔＩｎｔｈｉｓｐａｐ...     

Reflexivity of Operator Weighted Shifts

ＲｅｆｌｅｘｉｖｉｔｙｏｆＯｐｅｒａｔｏｒＷｅｉｇｈｔｅｄＳｈｉｆｔｓＬｉＪｕｅｘｉａｎ（李觉先）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬｉａｏｎｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｓｈｅｎｇｙａｎｇ，１１００３６）ＺｈａｏＴｉａｎｘｉａ（赵天霞...     

On Semi-weakly n-Hyponormal Weighted Shifts

Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W _α with α ₀ = α ₁ < α ₂ which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.