Fock型空间F1上的平移不变子空间的酉等价

考虑了Fock型空间F1上的平移不变子空间的酉等价问题,主要结果是如果F1的两个平移不变子空间作为子模酉等价,且其中之一具有形式span{∞ U k=1 eλkzPnk},则它们必定相等,还讨论了空间F1和Fg的关系,后者在物理学中有广泛的应用背景.     

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.     

C*-代数中的不变子空间问题

本文获得了下述结果设A是一可分的单C*-代数,对每个a(≠0)∈A,则都存在可分的忠实不可约*表示(π,Hπ),使得π(a)在Hπ中具有非平凡不变子空间.该结果完全解决了HuaxinLin[1]所提问题.     

Sobolev圆盘代数的不变子空间

本文研究了Sobolev圆盘代数R(D)上的乘法算子M_z的不变子空间,完全刻画了余维有限的不变子空间的结构．     

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。     

Invariant Subspaces for Pairs of Projections

A simple geometrical argument shows that every pair of projectionson a finite-dimensional complex vector space has a common invariantsubspace of dimension 1 or 2. The idea extends to certain pairsof projections on an infinite-dimensional Hilbert space H. Inparticular every projection on H has a reducing subspace, althougha finite-dimensional one need not exist. In a final section,the results are extended to the existence of hyperinvariantsubspaces for pairs of projections.     

Invariant Subspaces of Three-Dimensional Periodic Lightguides

A three-dimensional periodic lightguide is considered. Oscillations of the lightguide are described by the reduced wave equation. The existence of bounded projections onto invariant subspaces of the waveguide operator corresponding to intervals of the continuous spectrum is established. Bibliography: 6 titles     

Continuity of the Restriction of C 0-Semigroups to Invariant Banach Subspaces

A linear semigroup in a Banach space induces a linear semigroup on a Banach space that can be continuously embedded in the former such that its image is invariant. This restriction need not be strongly continuous, although the original semigroup is strongly continuous. We show that norm or weak compactness of partial orbits is a necessary and sufficient condition for strong continuity of the restriction of a C₀-semigroup. We then show that if the embedded Banach space is reflexive and the norms of the restricted semigroup operators are bounded near the initial time, then the restricted semigroup is strongly continuous.     

Stability of Invariant Subspaces of Quaternion Matrices

A quaternion invariant subspace of a quaternion matrix is said to be stable (in the sense of robustness) if every nearby matrix has an invariant subspace close to the original one. Under mild hypothesis, necessary and sufficient conditions are given for quaternion invariant subspaces to be stable. Other notions of stability of quaternion invariant subspaces are studied as well, and stability criteria developed. Applications to robustness of solutions of certain classes of quaternion matrix equations are given.     

p-Frames and Shift Invariant Subspaces of Lp

In this article we investigate the frame properties and closedness for the shift invariant space V_p(F) = { ?_i=1^r ?_{j ? \Zd} d_i(j) f_i (·-j):  ( d_i(j) )_{j ? \Zd} ? l^p }, \q 1 ￡ p ￡ ￥ . \displaystyle V_p(\Phi) = \left\{ \sum_{i=1}^r \sum_{j\in \Zd} d_i(j) \phi_i (\cdot-j): \ \left( d_i(j) \right)_{j\in \Zd}\in \ell^p \right\}, \q 1\le p \le \infty~. We derive necessary and sufficient conditions for an indexed family {f_i(·-j): 1 ￡ i ￡ r, j ? \Zd}\{\phi_i(\cdot-j):\ 1\le i\le r, j\in \Zd\} to constitute a pp-frame for V_p(F)V_p(\Phi), and to generate a closed shift invariant subspace of L^pL^p. A function in the L^pL^p-closure of V_p(F)V_p(\Phi) is not necessarily generated by l^p\ell^p coefficients. Hence we often hope that V_p(F)V_p(\Phi) itself is closed, i.e., a Banach space. For p 1 2p\ne 2, this issue is complicated, but we show that under the appropriate conditions on the frame vectors, there is an equivalence between the concept of pp-frames, Banach frames, and the closedness of the space they generate. The relation between a function f ? V_p(F)f \in V_p(\Phi) and the coefficients of its representations is neither obvious, nor unique, in general. For the case of pp-frames, we are in the context of normed linear spaces, but we are still able to give a characterization of pp-frames in terms of the equivalence between the norm of ff and an l^p\ell^p-norm related to its representations. A Banach frame does not have a dual Banach frame in general, however, for the shift invariant spaces V_p(F)V_p(\Phi), dual Banach frames exist and can be constructed.     

Invariant Subspaces for Semigroups of Algebraic Operators

T. Laffey showed (Linear and Multilinear Algebra6(1978), 269–305) that a semigroup of matrices is triangularizable if the ranks of all the commutators of elements of the semigroup are at most 1. Our main theorem is an extension of Hthis result to semigroups of algebraic operators on a Banach space. We also obtain a related theorem for a pair {A, B} of arbitrary bounded operators satisfying rank (AB−BA)=1 and several related conditions. In addition, it is shown that a semigroup of algebraically unipotent operators of bounded degree is triangularizable.     

\Pi_1空间上JC- 代数的不变子空间

讨论了\Pi_1空间上一般JC*-代数的不变子空间的存在条件问题,得到各类JC*-代数存在\Pi_1型不变子空间的等价条件.     

Invariant and Almost-Invariant Subspaces for Pairs of Idempotents

It is known that every bounded operator on an infinite dimensional separable Hilbert space \({\mathcal{H}}\) has an invariant subspace if and only if each pair of idempotents on \({\mathcal{H}}\) has a common invariant subspace. We show that the same equivalence holds for operators and pairs of idempotents that are essentially selfadjoint. We also show that each pair of idempotents on \({\mathcal{H}}\) has a common almost-invariant half-space.     

Sobolev圆盘代数的不变子空间

研究了Sobolev圆盘代数R(D)上乘自变量算子M_z的不变子空间,给出了M_z在任何不变子空间上限制的基本性质,证明了M_z分别限制在两个不变子空间上酉等价当且仅当这两个不变子空间相等,并描述了M_z的一类公共零点在边界的不变子空间的结构.     

Approximation of Invariant Subspaces in Some Dirichlet-Type Spaces

The Hilbert space \(\mathcal {D}_{2}\) is the space of all holomorphic functions f defined on the open unit disc \(\mathbb {D}\) such that \({f}^{'}\) is in the Hardy Hilbert space \(\mathbf {H}^2.\) In this paper, we prove that the invariant subspaces of \(\mathcal {D}_{2}\) with respect to multiplication operator \(M_{z}\) can be approximated with finite co-dimensional invariant subspaces. We also obtain a partial result in this direction for the classical Dirichlet space.     

多圆盘Hardy空间的不变子空间(英文)

设M是多圆盘Hardy空间H²（Tⁿ）的不变子空间.R_zi是以坐标函数z_i（i=1,2,…,n）为符号的乘法算子在M上的限制.本文作者证明了,存在一个内函数q,使得M=qH²（Tⁿ）当且仅当对i≠j,R_ziR_zj^*=R_zj^*R_zi.     

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.     

Multiplication Operators on Invariant Subspaces of Function Spaces

Let M_φ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator M_z, we derive some spectral properties of the multiplication operator M_φ : F → F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n ∈ {1, 2, …, + ∞}.     

Invariant Subspaces of Bergman Spaces on Slit Domains

In this paper, we characterize the z-invariant subspaces thatlie between the Bergman spaces A^p(G) and A^p(G\K), where 1 <p < , G is a bounded region in C, and K is a closed subsetof a simple compact C¹ arc.