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。     

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.     

Invariant and Hyperinvariant Subspaces of the Operator J α in Sobolev Spaces W p s [0,1]

Mathematical Notes -     

Some Isometric Properties of Subspaces of Function Spaces

We investigate the isometric properties of subspaces of Banach spaces which are unconditionally complemented in their biduals. In particular, we determine the fixed point properties for Müntz subspaces of dilation-stable weakly sequentially complete function spaces on [0, 1].     

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, …, + ∞}.     

奇特征有限正交空间中非迷向子空间的Critical问题

利用奇特征正交空间的性质及计数定理在奇特征正交空间中研究了非迷向子空间的Critical问题,得到了相应的计数公式和Critical指数.     

特征为2的有限正交空间上全奇异子空间的Critical问题

利用特征为2的有限正交空间的性质及计数定理在特征为2的有限正交空间上研究了全奇异子空间的Critical问题,得到了相应的计数公式和Critical指数.     

环内亚纯函数的特征函数

应用亚纯函数的Nevanlinna理论,研究了定义在圆环内的亚纯函数的特征函数.证明了定义在圆环内的具有最大亏量和的有限级允许亚纯函数f(名)与其各阶导函数f~((k))(z)的特征函数之间满足如下关系:当δ_0(∞,f)=1时,T_0(r,f~((k)))~T_0(r,f)(r→+∞);当δ_0(∞,f)=0时,T_0(r,f~((k)))~(k+1)T_0(r,f)(r→+∞),其中k为任意正整数.所得结果推广了定义在全平面上亚纯函数的一些相关结果.     

Hyperinvariant Closed Ideals for a Finitely Quasinilpotent Collection of Operators

Mathematical Notes - In this paper, it is proved that if $$\mathscr C\ne\{0\}$$ is a collection of continuous operators with modulus on an $$\ell_p$$ -space ( $$1\le p<\infty$$ ) that is...     

Contraction of Exterior Powers in Characteristic 2 and the Spin Module

Let K be a field of characteristic 2 and letV be a vector space of dimension 2m over K. Let f be a non-degenerate alternating bilinear form defined on V × V. The symplectic group Sp(2m, K) acts on the exterior powers ^k V for 0 k. 2m There is a contraction map defined on the exterior algebra , which commutes with the Sp(2m, K) action and satisfies ² = 0 and ( ^k V) ^k–1 V We prove that ( ^k V)= ker ^k–1 V except when k=m+2. In the exceptional case, ( ^m+2 V) has codimension 2^m in ker ^m V and we show that the quotient module ker ^m V/ ^m+2 V is a spin module for Sp(2m,K). When K is algebraically closed, we show that this spin module occurs with multiplicity 1 in ^m V and multiplicity 0 in all other components of V.     

Characteristic Function of a Pure Commuting Contractive Tuple

A theorem of Sz.-Nagy and Foias [9] shows that the characteristic function of a completely non-unitary contraction T is a complete unitary invariant for T. In this note we extend this theorem to the case of a pure commuting contractive tuple using a natural generalization of the characteristic function to an operator-valued analytic function defined on the open unit ball of This function is related to the curvature invariant introduced by Arveson [3].     

套代数子空间的端点

设d为套代数AlgN的子空间且包含AlgN的所有一秩算子．利用预零化子d⊥中一秩算子,我们给出了单位球d1中端点的刻画．     

Asymptotic Formulas and Inequalities for the Gamma Function in Terms of the Tri-Gamma Function

Results in Mathematics - In the paper, the authors establish some asymptotic formulas and double inequalities for the factorial n! and the gamma function Γ in terms of the tri-gamma function...     

利用特征为2域上伪辛几何中1维非迷向子空间构作PBIB设计

关于结合方案和PBIB设计的定义及所用的有关符号见文献[1].设F_q为特征为2的有限域,q=2~r.熟知F_q上的对称矩阵合同于以下三种形式的矩阵(见[1]p.24).     

特征函数的性质

得到了特征函数、条件特征函数的一致可微性和条件特征函数的反演公式.     

Subspaces with a Common Complement in a Separable Hilbert Space

We present an alternative proof of a characterization, due to M. Lauzon and S. Treil, of subspaces with a common complement in a separable Hilbert space. Our approach is motivated by known results concerning the relative position of two subspaces in a Hilbert space. As byproducts we obtain a simple example of a double triangle subspace lattice which is not similar to an operator double triangle and a characterization of pairs of subspaces in generic position which are not completely asymptotic to one another.      

Complemented Family of Subspaces of a Banach Space

In this article we investigate the connection between a family of complemented subspaces of a Banach space having a holomorphic basis, and being holomorphically complemented.     

Zeros of the Derivative of a Rational Function and Coinvariant Subspaces for the Shift Operator on the Bergman Space

If all n (n > 1) zeros of a rational function r with simple poles are in a half-plane, then the derivative of r has at least one zero in the same half-plane. This result is used to prove that the number of zeros of a linear combination of n Bergman kernels in the unit disk may range from 0 to 2n-3. Bibliography: 7 titles.