Nicolas Chevrot, Emmanuel Fricain, Dan Timotin
It is shown that a contraction on a Hilbert space is complex symmetric if and only if the values of its characteristic function are all symmetric with respect to a fixed conjugation. Applications are given to the description of complex symmetric contractions with defect indices equal to 2.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this note we study the completely non unitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions. These operators are precisely those which admit a matrix representation of the form T = S & * & * 0 & N & * 0& 0& C, where $S$ and C^* are unilateral shifts of arbitrary multiplicities and $N$ is nilpotent. We prove that dimension of ker S^* and dimension of ker C are unitary invariants of $T$ and that N, up to a quasi-similarity is uniquely determined by T. Also, we give a complete classification of the subclass of those contractions for which their…
Characteristic Functions and Colligations
利用配位理论重新证明了行收缩及其提升的特征函数的完全不变性，并刻画了具有特定基本算子的共等距可观测配位，研究了基于Blaschke因子的特征函数变换。
The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the following theorem: Let $T$ be a completely nonunitary contraction on a Hilbert space $\mathcal{H}$. If the characteristic function $Θ_T$ of $T$ is a polynomial of degree $m$, then there exist a Hilbert space $\mathcal{M}$, a nilpotent operator $N$ of order $m$, a coisometry $V_1 \in \mathcal{L}(\overline{ran} (I - N N^*) \oplus \mathcal{M}, \overline{ran} (I - T…
In this work, we give a description of Taylor spectrum of commuting 2- contractions in terms of characteristic functions of such contractions.The case of a single obtained by B.Sz.Nagy and C. Foias is generalised in this work.
$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions
本文研究希尔伯特空间中非稠定$C$-对称压缩算子的$C$-自伴压缩延拓，得到全部延拓的参数化形式，并应用该结果证明了Glazman提出的稠定$C$-对称耗散算子存在极大耗散$C$-自伴延拓的结论。
We review how some multianalytic inner functions of the Beurling type theorem are associated to row contractions following works of G.Popescu. Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. Our characteristic function is a complete unitary invariant for such tuples. Thereafter we extend the analysis of characteristic functions to contractive liftings of row contractions. We apply our theory to completely positive maps and explore applications t…
In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ in partially ordered metric spaces. The obtained results extend, complement and unify some recent coupled fixed point theorems due to Samet [B. Samet, \textit{Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces}, Nonlinear Anal. \textbf{72} (2010), 4508-4517], Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordere…
We prove that every generator of a symmetric contraction semigroup on a $σ$-finite measure space admits, for $1<p<\infty$, a Hörmander-type holomorphic functional calculus on $L^p$ in the sector of angle $ϕ^*_p=\arcsin|1-2/p|$. The obtained angle is optimal.
We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function is associated with any (constrained) row contraction. For pure constrained row contraction, we show that the characteristic function is a complete unitary invariant and provide a model. We also show that the curvature invariant and Euler characteristic asssociated with a Hilbert module generated by an arbitrary (resp. commuting) row contraction can be express…
A characteristic function is a special operator-valued analytic function defined on the open unit ball of $\mathbb{C}^n$ associated with an $n$-tuple of commuting row contraction on some Hilbert space. In this paper, we continue our study of the representations of $n$-tuples of commuting row contractions on Hilbert spaces, which have polynomial characteristic functions. Gleason's problem plays an important role in the representations of row contractions. We further complement the representations of our row contractions by proving theorems concerning factorizations of characteristic functions. …
Regularity of the Sz.-Nagy and Foiaş Factorization of Characteristic Functions and Its Multivariable Analogue
研究具有不变子空间的压缩算子和行压缩算子特征函数分解的正则性，构造反例说明一般非正则，给出正则性刻画，确定几类正则算子，引入\(k -\)奇异分解概念并证明特定压缩算子特征函数不存在\(k -\)奇异分解。
$k$-Regular Factorizations and Invariant Subspaces of Completely Non-Unitary Contractions
引入压缩算子的$k$-正则分解概念，建立其与完全非酉压缩的不变子空间链之间的一一对应，并构造显式泛函模型，同时引入交换$k$-压缩的对称$k$-正则元组，证明经典反例不满足该性质。
$k$-Regular Factorizations and Joint Invariant Subspaces of Completely Non-Coisometric Row Contractions
研究完全非等距行压缩的特征函数的$k$-正则分解，建立联合不变子空间链与$k$-正则分解的一一对应，并给出函数模型和块上三角分解。
We show that the constrained characteristic function is a complete unitary invariant for J-constrained completely non-coisometric (c.n.c.) row contractions, where J is a WOT-closed two-sided ideal of the noncommutative analytic Toeplitz algebra. We provide a model for this class of row contractions in terms of the constrained characteristic functions. In particular, we obtain a model theory for q-commuting c.n.c. row contractions.
Spectra of $1/k$-Contractions via Characteristic Functions
本文通过特征函数给出了欧几里得球上具有有限缺陷的 $1/k$-压缩算子的Taylor联合谱的下界估计，并在Corona性质下得到精确刻画，应用于CNP空间商模的谱确定。
The theory of characteristic functions for row contractions is used to determine the group $Aut(B(H)^n_1)$ of all free holomorphic automorphisms of the unit ball of $B(H)^n$. We show that the noncommutative Poisson transform commutes with the action of the automorphism group $Aut(B(H)^n_1)$. This leads to a characterization of the unitarily implemented automorphisms of the Cuntz-Toeplitz algebra $C^*(S_1,..., S_n)$, which leave invariant the noncommutative disc algebra $\cA_n$. This result provides new insight into Voiculescu's group of automorphisms of the Cuntz-Toeplitz algebra and reveals n…
The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $Λ$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.) $k$-tuples in ${\bf B}_Λ(H)$, and to study the characteristic functions and the associated multi-analytic models for the c.n.c. elements in the regular $Λ$-polyball. In addition, we show that the characteristic function is a complete unitary invariant for the class of c.n.c. $k$-tuples in ${\bf B}_Λ(H)$. These results extend the corresponding classical results of …
In this paper, we introduce a unitary invariant $Γ$ defined on the unit ball of $B(H)^n$ in terms of the characteristic function, the noncommutative Poisson kernel, and the defect operator associated with a row contraction. We show that $Γ$ detects the pure row isometries and completely classify them up to a unitary equivalence. We also show that $Γ$ detects the pure row contractions with polynomial characteristic functions and completely non-coisometric row contractions. In particular, we show that any completely non-coisometric row contraction with constant characteristic function is homogen…
Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a "one-to-one" correspondence between the joint invariant subspaces under T_1,..., T_n, and the regular factorizations of the characteristic function associated with T. In particular, we prove that there is a non-trivial joint invariant subspace under the operators T_1,..., T_n, if and only if there is a non-trivial regular factorization of the characteristic function. We also provide a functional model for the joint invariant subspaces …
In the deBranges-Rovnyak functional model for contractions on Hilbert space, any completely non-coisometric (CNC) contraction is represented as the adjoint of the restriction of the backward shift to a deBranges-Rovnyak space, $\mathscr{H} (b)$, associated to a contractive analytic operator-valued function, $b$, on the open unit disk. We extend this model to a large class of CNC row contractions of several copies of a Hilbert space into itself (including all CNC row contractions with commuting component operators). Namely, we completely characterize the set of all CNC row contractions, $T$, wh…
Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate their behavior. We study the convergence of the Picard iteration to a fixed point of such an operator under different types of generalized contraction conditions. The obtained results may have interesting practical applications in various research areas.
Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G. Popescu. We prove that our characteristic function is a complete unitary invariant for such tuples and show how it can be computed.
Consider --- for the generator \({-}A\) of a symmetric contraction semigroup over some measure space $\mathrm{X}$, $1\le p < \infty$, $q$ the dual exponent and given measurable functions $F_j,\: G_j : \mathbb{C}^d \to \mathbb{C}$ --- the statement: $$ \mathrm{Re}\, \sum_{j=1}^m \int_{\mathrm{X}} A F_j(\mathbf{f}) \cdot G_j(\mathbf{f}) \,\,\ge \,\,0 $$ {\em for all $\mathbb{C}^d$-valued measurable functions $\mathbf{f}$ on $\mathrm{X}$ such that $F_j(\mathbf{f}) \in \mathrm{dom}(A_p)$ and $G_j(\mathbf{f}) \in \mathrm{L}^q(\mathrm{X})$ for all $j$.} It is shown that this statement is valid in ge…
A new functional model for contractions
本文利用对称算子扩张理论的共同几何基础，为完全非酉压缩算子提出一种内蕴、规范构造且不依赖特征函数的新泛函模型。
Some fixed points results for extended nonlinear contractions defined on $d-CS$ spaces
本文引入d-CS空间类并建立其拓扑框架，证明非线性扩展压缩映射的不动点定理，统一推广了拟b-度量空间、b-空间及拟度量空间中的多项经典结果。
A non-commutative de Branges-Rovnyak model for row contractions
本文提出非交换德布兰-罗文纳克模型，用于描述CNC行收缩的特征函数及其单位不变性。
Vector valued de Branges spaces, CNU contractions and functional models
本文通过Hilbert空间直和分解构造向量值再生核Hilbert空间，证明其为de Branges空间，并用于建立完全非酉压缩算子的函数模型，同时给出Fredholm型判据并建立特征函数与投影算子值函数的关系。
Let $A = (A_1, \ldots, A_n)$ and $B = (B_1, \ldots, B_n)$ be row contractions on $\mathcal{H}_1$ and $\mathcal{H}_2$, respectively, and $X$ be a row operator from $\oplus_{i=1}^n \mathcal{H}_2$ to $\mathcal{H}_1$. Let $D_{A^*} = (I - A A^*)^{\frac{1}{2}}$ and $D_{B} = (I - B^* B)^{\frac{1}{2}}$ and $Θ_T$ be the characteristic function of $T = \begin{bmatrix} A& D_{A^*}L D_B\\ 0 & B \end{bmatrix}$. Then $Θ_T$ coincides with the product of the characteristic function $Θ_A$ of $A$, the Julia-Halmos matrix corresponding to $L$ and the characteristic function $Θ_B$ of $B$. More precisely, $Θ_T$ coi…
For a fixed natural number n, we consider a family of rank n unitary perturbations of a completely non-unitary contraction (cnu) with deficiency indices (n,n) on a separable Hilbert space. We relate the unitary dilation of such a contraction to its rank n unitary perturbations. Based on this construction, we prove that the spectra of the perturbed operators are purely singular if and only if the operator-valued characteristic function corresponding to the unperturbed operator is inner. In the case where n=1 the latter statement reduces to a well-known result in the theory of rank one perturbat…
This note finds a new characterization of complete Nevanlinna-Pick kernels on the Euclidean unit ball. The classical theory of Sz.-Nagy and Foias about the characteristic function is extended in this note to a commuting tuple $\bfT$ of bounded operators satisfying the natural positivity condition of $1/k$-contractivity for an irreducible unitarily invariant complete Nevanlinna-Pick kernel. The characteristic function is a multiplier from $H_k \otimes \cE$ to $H_k \otimes \cF$, {\em factoring} a certain positive operator, for suitable Hilbert spaces $\cE$ and $\cF$ depending on $\bfT$. There is…
Characteristic function of a power partial isometry
本文基于Sz.-Nagy-Foiaş模型理论，完整分类了与c.n.u.幂部分等距关联的纯压缩解析函数，并刻画了使Toeplitz算子成为部分等距的算子值符号。
The main aim of this paper is to establish the connection between well-known criteria for the pseudocontinuability of a non-inner Schur function Theta in the unit disk. In a canonical way we associate a probability measure mu on the unit circle with Theta. One of the two criteria will be reformulated in the face of mu, whereas the other one is drafted in view of a completely non--unitary contraction T having Theta as its corresponding characteristic function. Our main result clarifies an immediate connection between the above-mentioned two criteria. For this reason, we construct a special orth…
A bounded linear operator $T$ on a Hilbert space is said to be homogeneous if $φ(T)$ is unitarily equivalent to $T$ for all $φ$ in the group Möb of bi-holomorphic automorphisms of the unit disc. A projective unitary representation $σ$ of Möb is said to be associated with an operator T if $φ(T)= σ(φ)^\star T σ(φ)$ for all $φ$ in Möb. In this paper, we develop a Möbius equivariant version of the Sz.-Nagy--Foias model theory for completely non-unitary (cnu) contractions. As an application, we prove that if T is a cnu contraction with associated (projective unitary) representation $σ$, then there …
The characteristic function for a contraction is a classical complete unitary invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to the Szego kernel $k_S(z,w) = (1 - z\ow)^{-1}$ for $|z|, |w| < 1$, by means of $(1/k_S)(T,T^*) \ge 0$, we consider an arbitrary open connected domain $Ω$ in $\BC^n$, a complete Nevanilinna-Pick kernel $k$ on $Ω$ and a tuple $T = (T_1, ..., T_n)$ of commuting bounded operators on a complex separable Hilbert space $\clh$ such that $(1/k)(T,T^*) \ge 0$. For a complete Pick kernel the $1/k$ functional calculus makes sense in a beautiful way. It t…
Complete Nevanlinna-Pick property of $\mathbb K$-Invariant Reproducing Kernels
本文研究了$\mathbb K$-不变再生核的完整Nevanlinna-Pick性质，通过扩展特征函数概念并构造显式特征函数，给出了具有该性质的核的特征化条件。
We develop a Sz.-Nagy--Foias-type functional model for a commutative contractive operator tuple $\underline{T} = (T_1, \dots, T_d)$ having $T = T_1 \cdots T_d$ equal to a completely nonunitary contraction. We identify additional invariants ${\mathbb G}_\sharp, {\mathbb W}_\sharp$ in addition to the Sz.-Nagy--Foias characteristic function $Θ_T$ for the product operator $T$ so that the combined triple $({\mathbb G}_\sharp, {\mathbb W}_\sharp, Θ_T)$ becomes a complete unitary invariant for the original operator tuple $\underline{T}$. For the case $d \ge 3$ in general there is no commutative isome…
The normal contraction property for non-bilinear Dirichlet forms
本文研究Cipriani和Grillo提出的非双线性Dirichlet型的正规收缩性质，证明该性质成立等价于泛函对称，且仅需验证双参数函数族即可，丰富了非双线性Dirichlet型的理论研究。
Positive definite functions of noncommuting contractions, Hua-Bellman matrices, and a new distance metric
本研究纠正了Bellman关于Hua-Bellman矩阵正定性的错误证明，给出正定函数的精确条件，并引入非交换压缩算子上的新距离度量。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。