关于序列次可分解算子的不变子空间

得到了关于序列次可分解算子的一个不变子空间定理，推广了H.Mohebi和M.Rajiabalipour在1994年得到的一个不变子空间定理，并且举例说明存在l2上的有界线性算子T。它有无穷多个变子空间，但是它的不变子空间格Lat(T)不丰富。     

序列次可分解算子的不变子空间格

本文研究了序列次可分解算子的不变子空间问题,得到了一类序列次可分解算子具有丰富的不变子空间格的结果,精细地刻划了这类序列次可分解算子的不变子空间格.     

序列次可分解算子的不变子空间格

本文研究了序列次可分解算子的不变子空间问题，得到了一类序列次可分解算子具有丰富的不变子空间格的结果，精细地刻划了这类序列次可分解算子的不变子空间格．     

关于压缩算子的不变子空间

证明关于压缩算子的如下不变子空间定理：如果T是Hilbert空间H上的压缩算子,且集合Z’={λ∈D;存在z∈H,使得‖z‖=1,且‖（λ-T）z‖＜1/3(1-‖λ‖}是开单位圆D的控制集,那么T有非平凡的不变子空间,这个定理包含了S.Brown,B.Chevreau,C.fPearcy和B.Beauzamy的两个重要结果作为特殊情况,特别是,为个定理包含了S.Brown等人的Hilbert空间上的每个具有厚谱的压缩算子都有平凡的不变子空间这个重要结果作为特殊情况。     

某些加权复合算子之不变子空间的存在性

本文研究某些加权复合算子之非平凡不变子空间的存在性.特别地,证明了每个亚正规加权复合算子均有非平凡的不变子空间并且提出了一个新概念,称其为本性可逆变换.对于概率空间上本性可逆变换所确定的加权复合算子,给出其非平凡不变子空间存在性的一个等价刻画.     

某些加权复合算子之不变子空间的存在性

本文研究某些加权复合算子之非平凡不变子空间的存在性。特别地,证明了每个亚正规加权复合算子均有非平凡的不变子空间并且提出了一个新概念,称其为本性可逆变换。对于概率空间上本性可逆变换所确定的加权复合算子,给出其非平凡不变子空间存在性的一个等价刻画。     

Krein空间中无穷维Hamilton算子的极大确定不变子空间的存在性问题

本文研究了不定度规空间空间中的无穷维Hamilton算子.利用Plus算子存在极大不变子空间的性质,获得了无穷维Hamilton算子在Krein空间中存在极大确定不变子空间的充分条件.     

一些新的单胞算子及可达全序格

本文构造了一类新的单胞算子,全部刻划了它们的不变子空间,并证明了,对任意正整数m及任意幂零算子的不变子空间格,格是可达的,特别地,对任意正整数是可达全序格。     

多圆盘的加权Bergman空间上的不变子空间和约化子空间

本文主要研究多圆盘的加权Bergman 空间上的不变子空间和约化子空间, 给出了某些解析Toeplitz 算子的极小约化子空间的完全刻画, 以及一类解析Toeplitz 算子Tzi (1≤i≤n) 的不变子空间的Beurling 型定理.     

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.     

On the distance between lattices of invariant subspaces of matrices

We study the behavior of the lattice Inv(X) of all invariant subspaces of a matrix X, when X belongs to the class of matrices with fixed Jordan structure (i.e., with isomorphic lattices of invariant subspaces). A larger class of matrices with fixed Jordan structure corresponding to the eigenvalues of geometric multiplicity greater than one is also studied. Our main concern is analysis of the distance between the lattices of invariant subspaces.     

The lattices of invariant subspaces of a class of operators on the Hardy space

In the authors’ first paper, a Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra operator. The current work is an extension of the previous work and it describes the lattice of invariant subspaces of the shift plus a positive integer multiple of the complex Volterra operator on the Hardy space. Our work was motivated by a paper by Ong who studied the real version of the same operator.     

Structural matrix algebras related to finite distributive lattices

Abstract

In this paper, we investigate the relation between a structural matrix algebra and the lattice properties of its lattice of invariant subspaces, and reprove known results in a fresh and an explanatory way. Moreover, we also prove the theorem which is partially converse of Proposition 2.6 of [15].     

Invariant Subspaces for Compact-Friendly Operators in Sobolev Spaces

In this note we extend the concept of compact-friendlyness, defined in the literature for operators on a Banach lattice, to the case of operators on Sobolev spaces and derive the existence of invariant subspaces for compact-friendly operators of this type.     

Invariant subspaces of positive strictly singular operators on Banach lattices

It is shown that every positive strictly singular operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly singular and a regular AM-compact operator is strictly singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly operators can be extended to strictly singular-friendly operators.     

Invariant subspaces for translation,dilation and multiplication semigroups

We study invariant subspaces in the context of the work of Katavolos and Power [9] and [10] when one of the semigroups considered is replaced by a discrete one. As a consequence, a rather striking connection is given with the study of the lattice of invariant subspaces of composition operators induced by automorphisms of the unit disc acting on the classical Hardy space. As a particular instance, our study concerns the lattice of invariant subspaces of those composition operators induced by hyperbolic automorphisms, and therefore with the Invariant Subspace Problem. Partially supported by Plan Nacional I+D grant no. MTM2006-06431 and Gobierno de Aragón research group Análisis Matemático y Aplicaciones, ref. DGA E-64.     

A Class of C ·0-Contractions: Hyperinvariant Subspaces and Intertwining Operators

We consider a class of C_·0-contractions that is a generalization of the class of C_·0-contractions with finite defect indices. Some results of Uchigama and Wu for C_·0-contractions with finite defect indices are generalized: the lattices of hyperinvariant subspaces of such a contraction T is isomorphic to that of its Jordan model and is generated by subspaces of the form Ker ϕ(T) and Ran ϕ(T), where ϕ ∈ H^∞. The form of the inverse to an isomorphism of the invariant subspace lattices given by an intertwining quasiaffinity is also studied. Next, for C_·0-contractions in question, the characteristic disc related to the lattice of invariant subspaces is computed. Bibliography: 13 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 315, 2004, pp. 48–62.     

A cross section from invariant subspaces to inner functions

Beurling's well known theorem connects the study of invariant subspaces to that of inner functions over the unit disc. In this paper, we will further explore this connection and, as a corollary of the result, show a one to one correspondence between the components of the invariant subspace lattice and the components of the space of inner functions.     

The invariant subspaces of the shift plus integer multiple of the Volterra operator on Hardy spaces

?u?kovi? and Paudyal recently characterized the lattice of invariant subspaces of the shift plus a complex Volterra operator on the Hilbert space \(H^2\) on the unit disk. Motivated by the idea of Ong, in this paper, we give a complete characterization of the lattice of invariant subspaces of the shift operator plus a positive integer multiple of the Volterra operator on Hardy spaces \(H^p\), which essentially extends their works to the more general cases when \(1\le p<\infty \).