N重加权移位算子的拟相似和谱

本文给出了n重内射加权移位算子拟相似的充要条件,完全刻划了它们之间的拟相似结构,由此得到,拟相似的n重内射单边加权移位是相似的;拟相似的n重内射双边加权移位不必是相似的,但有相同的谱,这些结果分别推广了[5,6,8]中的相关结果。     

加权 N 移位算子的约化子空间格和不变子空间格

本文对有限加权 N 移位算子的约化子空间格和不变子空间格给出了具体的构造.进而,我们给出了几个判断有限加权 N 移位算子为不可约算子的充分条件.     

符号空间的拟移位和Mǒbius带上的奇怪吸引子

给出了双边符号空间上的一种新的拟移位映射,得到了它与传统的移位映射拓扑共轭.类似Smale马蹄,对这种拟移位映射给出了一个模型,即在M(o)bius带上给出一类映射.同时刻划了这类映射的吸引子的结构及动力学行为.     

单位球上加权Bergman空间中乘子算子的拟相似性

给定α＞-1,令A2α(B N)表示N维复平面CN中单位开球BN上的加权Bergman空间.本文证明了在A2α(B N)中,乘子算子Mzn拟相似于⊕ΠNi=11ni Mz,其中n=(n1,n2,...,nN)为多重指标.     

关于态射的加权Moore-Penrose逆

研究了范畴中态射 f关于态射β和γ的加权 Moore-Penrose逆 fβ,γ+,分别给出了一般态射、有满单分解态射与有核 (上核 )的 fβ,γ+存在的充要条件及其相应的表达式 ,推广了 f关于对称态射β和γ的加权Moore-Penrose逆的相应结果 .     

符号空间的拟移位和Moebius带上的奇怪吸引子

给出了双边符号空间上的一种新的拟移位映射，得到了它与传统的移位映射拓扑共轭．类似Smale马蹄，对这种拟移位映射给出了一个模型，即在Moebius带上给出一类映射．同时刻划了这类映射的吸引子的结构及动力学行为．     

符号空间的拟移位和Mbius带上的奇怪吸引子

给出了双边符号空间上的一种新的拟移位映射,得到了它与传统的移位映射拓扑共轭·　类似Smale马蹄,对这种拟移位映射给出了一个模型,即在M bius带上给出一类映射·　同时刻划了这类映射的吸引子的结构及动力学行为·     

态射集中的加权星序和加权广义逆

本文推广范畴上态射集中的星序理论.引进范畴上态射集中的加权星序.利用态射集的加权广义逆来刻划态射集中的加权星序.给出了态射集中的加权星序和态射的加权广义逆之间的一些关系.得到了态射集中的加权星序的一些刻划和性质.     

B(X)上保持算子拟仿射性或值域稠性的线性映射

设X和y是无限维的复Banach空间,φ是从B(X)到B(y)保单位的线性满射.本文证明了φ双边保算子的拟仿射性当且仅当φ为同构或反同构;φ双边保算子的值域稠性当且仅当φ是同构.     

B(X)上保持算子拟仿射性或值域稠性的线性映射

设X和Y是无限维的复Banach空间,Φ是从B(X)到B(Y)保单位的线性满射.本文证明了Φ双边保算子的拟仿射性当且仅当Φ为同构或反同构;Φ双边保算子的值域稠性当且仅当Φ是同构.     

加权移位算子的拟相似与谱

加权移位算子的拟相似与谱许凤，卢玉峰（东北师范大学数学系，长春１３００２４）１９９１年１２日２４日收到．设Ｈ是复可分Ｈｉｌｂｅｒｔ空间，Ｌ（Ｈ）表示Ｈ上有界线性算子全体，Ｚ是整数全体，Ｚ＋是非负整数全体，Ｉ＝Ｚ或Ｚ是Ｈ的正规正交基，是有界数列，Ｋ是一...     

The Single Valued Extension Property for Operator Weighted Shifts

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On the (U+K)-orbits of certain weighted shifts

D. A. Herrero has defined the (U+K)-orbit of an operatorT acting on an Hilbert space as (U+K)(T)={R ^–1 TR: R invertible of the form unitary plus compact}. In this paper we consider the (U+K)-orbit and the closure thereof for bilateral and unilateral weighted shifts. In particular, we determine which shifts are in the (U+K)-orbits of injective weighted shifts and which shifts are in the closure of the (U+K)-orbit of periodic injective shifts. Also, the closure of the (U+K)-orbit of injective essentially normal shifts is determined.Research supported in part by an NSERC operating grant.     

DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space.The disjoint supercyclic properties of weighted translations on locally compact discrete groups,the direct sums of finite classical weighted backward shifts, and the bilateral backward operator weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space ?~2(Z) never satisfy the d-Supercyclicity Criterion by a simple proof.     

K 0-group and similarity of operator weighted shifts

By using simultaneous triangularization technique, similarity for operator weighted shifts with finite multiplicity is characterized in terms of K0-group of commutant algebra. The result supports the conjecture posed by Cao et al. in 1999. Moreover, we discuss the relations between similarity and quasi-similarity for operator weighted shifts.     

Compressions of Stable Contractions

The stability of compressions of stable contractions is studied and a sufficient orbit condition is given. On the other hand, it is shown that there are non-stable compressions of the 1-dimensional backward shift and a complete characterization of weighted unilateral shifts with this property is provided. Dilations of bilateral weighted shifts to backward shifts are also considered.     

算子权移位的Banach约化性

本文给出了单边算子权移位是ＢＲ算子的充要条件及双边算子权移位是ＢＲ算子的充分条件．做为推论，重新得到了［１］中的一个结果，并得到了一类ＢＩＲ单边算子权移位的例子。最后，给出大量的ＨＩＲ但同时又是ＢＲ的单边算子权移位。     

Orthogonal decompositions for wavelets

Decompositions of Hilbert spaces in terms of reducing subspaces for wavelets operators, as well decompositions of these operators themselves, are investigated. In particular, it is shown on which reducing subspaces these operators act as bilateral shifts of multiplicity 1. We also exhibit the unitary transformation that performs the unitary equivalence between restrictions of them to appropriate reducing subspaces.     

The homogeneous shifts

A bounded linear operator T on a complex Hilbert space is called homogeneous if the spectrum of T is contained in the closed unit disc and all bi-holomorphic automorphisms of this disc lift to automorphisms of the operator modulo unitary equivalence. We prove that all the irreducible homogeneous operators are block shifts. Therefore, as a first step in classifying all of them, it is natural to begin with the homogeneous scalar shifts.In this paper we determine all the homogeneous (scalar) weighted shifts. They consist of the unweighted bilateral shift, two one-parameter families of unilateral shifts (adjoints of each other), a one-parameter family of bilateral shifts and a two-parameter family of bilateral shifts. This classification is obtained by a careful analysis of the possibilities for the projective representation of the Möbius group associated with an irreducible homogeneous shift.     

A uniqueness theorem for representations of GSO(6) and the strong multiplicity one theorem for generic representations of GSp(4)

Consider the θ-correspondence from GSp(4) to GSO(6). We prove that locally over a nonarchimedean fieldF, this correspondence is injective on generic representations (i.e. with Whittaker model) of GSp(4,F). We use this to show the strong multiplicity one property for irreducible, automorphic, cuspidal representations of GSp(4,A), which are generic.