Ikram Fatima Zohra Bensaid, Souheyb Dehimi, Bent Fuglede, Mohammed Hichem Mortad
In this paper, we show a new and classic version of the celebrated Fuglede Theorem in an unbounded setting. A related counterexample is equally presented. In the second strand of the paper, we give a pair of a closed and self-adjoint (unbounded) operators which is not intertwined by any (bounded or closed) operator except the zero operator.
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Asymmetric Fuglede Putnam's Theorem for operators reduced by their eigenspaces
Fuglede-Putnam定理在相当多的算子类中得到了证明。本文利用谱理论得到了一个理论上的一般框架，由此可以迅速地建立许多类算子的Fuglede-Putnam定理。
Fuglede-Putnam theorem is not true in general for $ EP $ operators on Hilbert spaces. We prove that under some conditions the theorem holds good. If the adjoint operation is replaced by Moore-Penrose inverse in the theorem, we get Fuglede-Putnam type theorem for $ EP $ operators -- however proofs are totally different. Finally, interesting results on $ EP $ operators have been proved using several versions of Fuglede-Putnam type theorems for $ EP $ operators on Hilbert spaces.
In this note a Fuglede type theorem is proved for Fourier multiplier operators on translation invariant Banach function spaces with order continuous norm over compact abelian groups.
In this article, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem. As applications, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.
Fuglede theorem for symmetric spaces of $τ$-measurable operators
本文将经典Fuglede定理扩展到对称规范算子理想，提出τ-可测算子对称空间满足Fuglede定理的充要条件，涵盖Lorentz和Schatten类等已知情况。
Operator synthesis II. Individual synthesis and linear operator equations
我们的工作的第二部分算子合成涉及个别算子合成的元素在一些张量积，特别是在Varopoulos代数，其连接与线性算子方程。使用一种发展的技术"近似逆交织“，我们得到一些推广的Fuglede和Fuglede-Weiss定理。此外，我们给出了一些应用程序的谱综合Varopoulos代数和偏微分方程。
In this note, we give the most natural (perhaps the simplest ever) generalization of the Fuglede-Putnam theorem where all operators involved are unbounded.
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
In this paper, we show that Orlicz--Sobolev spaces $W^{1,ϕ}(Ω)$ can be characterized with the ACL- and ACC-characterizations. ACL stands for absolutely continuous on lines and ACC for absolutely continuous on curves. Our results hold under the assumptions that $C^1(Ω)$ functions are dense in $W^{1,ϕ}(Ω)$, and $ϕ(x,β) \geq 1$ for some $β> 0$ and almost every $x \in Ω$. The results are new even in the special cases of Orlicz and double phase growth.
We present how to apply a Berberian's technique to asymmetric Putnam-Fuglede theorems. In particular, we proved that if $A, B \in B(H)$ belong to the union of classes of $*$-paranormal operators, p-hyponormal operators, dominant operators and operators of class Y and $AX = XB^*$ for some $X \in B(H)$, then $A^*X = XB$. Moreover, we gave a new counterexample for an asymmetric Putnam-Fuglede theorem for paranormal operators
Applications of the Fuglede-Kadison determinant: Szegö's theorem and outers for noncommutative $H^p$
我们首先利用有限von Neumann代数$M$的Fuglede-Kadison行列式在$L^p(M)$上的性质，给出了$L^p(M)$的非交换Szegö定理的几个有用的变体，包括通常归因于Kolmogorov和Krein的一个.作为一个应用，我们解决了长期开放的问题有关的非交换推广，Arveson的非交换$H^p$空间，著名的“外因式分解”的功能$f$与$\log |f|$可积。利用Fuglede-Kadison行列式，我们还推广了许多其他关于外函数的经典结果。
A closed densely defined operator $ T $ on a Hilbert space $ \mathcal{H} $ is callled $M$-hyponormal if $\mathcal{D}(T) \subset \mathcal{D}(T^{*}) $ and there exists $ M > 0 $ for which $ \parallel(T-zI)^{*}x \parallel \leq M \parallel(T-zI)x \parallel $ for all $ z \in \mathbb{C}$ and for all $ x\in \mathcal{D}(T)$. In this paper, we prove that if bounded linear operator $ A : \mathcal{H} \rightarrow \mathcal{K}$ is such that $ AB^*\subseteq TA $, where $ B $ is a closed subnormal (resp. a closed $ M $-hyponormal) on $\mathcal{H}$, $ T $ is a closed $ M $-hyponormal (resp. a closed subnormal)…
The Sum of Two Unbounded Linear Operators: Closedness, Self-adjointness and Normality
本文给出了两个无界算子和的闭性与自伴性的结果。我们提出了一个新的方法来解决这些基本问题的算子理论。我们还证明了一个新版本的Fuglede定理，其中涉及的运营商都是无界的。这个新的Fuglede定理允许我们证明（在额外的条件下）两个无界正规算子的和保持正规。作为这个新的“Fuglede定理”的一个结果，还得到了两个正规算子的无界积的正规性。还给出了一些有趣的例子。
Fuglede-Putnam type theorems via the Aluthge transform
令$A=U|A|$和$B=V|B|$是$A\in \mathbb{B}(\mathscr{H}_1)$和$B\in \mathbb{B}(\mathscr{H}_2)$的极分解，并令$Com(A,B)$代表算子集合$X\in\mathbb{B}(\mathscr{H}_2,\mathscr{H}_1)$，使得$AX=XB$。如果$Com(A,B)\subseteqCom(A^\ast,B^\ast)$，则称一对$(A,B)$具有FP性质。设$\tilde{C}$表示有界线性算子$C$的高斯变换.证明了：（i）若$A$和$B$可逆且$(A,B)$具有FP-性质，则$(\tilde{A},\tilde{B})$也可逆;（ii）若$A$和$B$可逆且$U$和$V$的谱都包含在某个开循环中且$(\tilde{A},\tilde{B})$具有FP-性质，则$(A,B)$也可逆;（iii）如果$(A,B)$具有FP性质，则为$Com(A,B)\subseteqCom(\tilde{A},\tilde{B})$，此外，如果$A$可逆，则为$Com(A,B)=Com(\tilde{A},\tilde{B})$。最后，如果$Re(U|A|^{1\over2})\geq a>0$和$Re(V|B|^{1\over2})\geq a>0$和$X$是一个算子，使得$U^* X=XV$，那么我们证明了$\|…
Following Beurling's theorem the natural compressions of the multiplication operator in the classical $L^2$ space are compressions to model spaces and to their orthogonal complements. Two possibly different model spaces are considered hence asymmetric truncated Toeplitz and asymmetric dual truncated Toeplitz operators are investigated. The main purpose of the paper is to characterize operators which intertwine compressions of the unilateral shift.
There are several proofs of the classical commutant lifting and intertwining lifting theorems in the literature. In this article, we present analogous proofs to a few $Q$-commuting lifting and $Q$-intertwining lifting theorems. We provide several proofs and show explicit constructions of Ando-type dilations for a pair of $Q$-commuting contractions $(T_1,T_2)$ when $Q$ is a bounded operator. We establish a few connections of these results with graph theory.
Starting from Sinclair's 1976 work {\it Automatic Continuity of Linear Operators}, Cambridge University Press, (1976), on automatic continuity of linear operators on Banach spaces, we prove that sequences of intertwining continuous linear maps are eventually constant with respect to the separating space of a fixed linear map. Our proof uses a gliding hump argument. We also consider aspects of continuity of linear functions between locally convex spaces and prove that such that a linear function $T$ from the locally convex space $X$ to the locally convex space $Y$ is continuous whenever the sep…
Monogenic Calculus as an Intertwining Operator
我们修改了单演演算几个非交换运营商，这是通过群表示定义。代替代数同态，我们使用组协方差。讨论了联合谱的有关概念和谱映射定理。构造说明了一个简单的例子，微积分和联合频谱的两个非交换自伴（n \times n）矩阵。关键词：泛函微积分，谱，交织算子，谱映射定理，喷流空间，单演函数，Clifford代数
General explicit expressions for intertwining operators and direct rotations of two orthogonal projections
本文基于块算子技巧和算子谱理论，建立了两个正交投影的交织算子和正旋转的一般显式表达式。因此，它是Kato的结果（线性算子的扰动理论，Springer-Verlag，Berlin/Heidelberg，1996）; Seiler和B. Simon定理2.3（一对投影的索引，J. Funct. Anal. 120（1994）220-237）和C. Davis，W. M. Kahan，（本征向量的扰动旋转，III。SIAM J. Numer. Anal. 7（1970）1-46）。
Positive definite maps, representations and frames
我们提出了一个单一的方法来建设的表示和交织运营商。我们把它应用到$C^*$ -代数、群、Gabor型酉系和小波上。我们给我们的方法的框架理论的应用程序，我们证明了一般的膨胀定理，这反过来又适用于特定的情况下，我们得到这样的小波膨胀定理。
Spectrum as the Support of Functional Calculus
本文利用SL 2（R）的表示论研究了解析谓词演算的新定义.我们避免了任何使用其代数同态性质，并取代它的要求是一个交织算子。给出了谱的相关概念和谱映射定理。通过一个简单的非正规n × n矩阵的微积分和谱的例子说明了这种构造。关键词：谓词演算，谱，交织算子，谱映射定理，喷流空间。
On a family of differential-reflection operators: intertwining operators and Fourier transform of rapidly decreasing functions
我们引入一个家庭的微分反射运营商$Λ_{A, \varepsilon}$作用于$\mathbb R.$上定义的光滑函数在这里$A$是一个斯特拉姆-刘维函数与额外的假设和$\varepsilon\in \mathbb R.$对于特殊的对$(A,\varepsilon),$，我们恢复Dunkl的，赫克曼的和Cherednik的运营商（在一维）。研究了算子$Λ_{A, \varepsilon}$的谱问题.特别是，我们得到合适的增长估计的特征函数的$Λ_{A, \varepsilon}$。由于算子$Λ_{A, \varepsilon}$是$d/dx$和反射算子的混合算子，我们证明了$Λ_{A, \varepsilon}$和通常导数之间存在一个交织算子$V_{A,\varepsilon}$.还建立了$V_{A,\varepsilon}$的阳性。通过$Λ_{A,\varepsilon},$的特征函数，我们引入了一个广义的傅里叶变换$\mathcal F_{A,\varepsilon}.$.当$0<p\leq {2\over{1+\sqrt{1-\varepsilon^2}}}$和$-1\leq \varepsilon\leq 1.$时，对$\mathcal F_{A,\varepsilon}$进行了$L^p$ -调和分析，并证明了$\mathcal F_{A,\varepsilon}$的$L^…
A well-known theorem due to R. E. Curto and N. Salinas gives a necessary and sufficient condition for the unitary equivalence of commuting tuples of bounded linear operators acting on reproducing kernel Hilbert spaces. Inspired by this theorem, we obtain a different but equivalent criterion for the unitary equivalence of operators acting on reproducing kernel Hilbert spaces. As an application, we describe the structure of intertwining operator and prove that the decomposition of Cowen-Douglas operators is unique up to unitary equivalence.
Quantitative BT-Theorem and automatic continuity for standard von Neumann algebras
本文证明了冯诺依曼代数$M$为标准型的一般判据。它是制定在一个处处定义的，可逆的，反线性的，先验的不一定有界算子，交织$M$与它的交换子$M'$和作为$*$ -操作的中心。我们还证明了一个广义版本的BT定理，使我们能够看到，这样的缠绕必须有界。它表明，BT定理的这一扩展导致相当一般的运营商的自动有界性，这interrupt的身份映射的von Neumann代数与一般有界的，真正的线性，运营商值的映射。我们应用最后的结果实现代数态射的冯诺依曼代数到一些Banach代数的线性算子的自动有界性，并赋予一个正常的，半有限的，忠实的重量$W^*$，其左理想$\mathfrak N_φ$承认在GNS表示空间$H_φ\,$代数补的$M$的结构，不变的规范作用下的$M$。
Ando dilations and inequalities on noncommutative domains
本文得到了非交换正则域D_f和非交换算子簇V_J的缠绕扩张定理，推广了Sarason和Sz.可换压缩的Nagy-Foias可换提升定理。本文给出了几个应用，其中包括对域D_f中纯元的交换提升定理的一个新证明。Variety V_J）的单位球的Schur型表示.我们给出了双整环D_f \times D_g和双簇V_J \times V_I的Ando型扩张和不等式.特别地，我们得到的扩展Ando的结果和Agler-McCarthy不等式的交换压缩到更大的类的交换运营商。
Entropy and multivariable interpolation
本文对Fock空间上的算子和自由半群上的正定多Toeplitz核定义了一个新的熵概念。这是研究与因式分解定理（多Toeplitz，多解析等）。Fock空间上的算子这些结果导出了自由半群上正定多Toeplitz核（多Toeplitz算子）的熵不等式和熵公式，以及非交换解析Toeplitz代数F_n^ \infty的单位球极值点的一些结果.我们得到了多变量中心缠绕提升的几个几何特征，一个最大值原理，和一个非对易交换提升定理的持久性原理。在一定的自然条件下，我们发现这个多变量交换提升定理的最大熵解（及其熵）的显式形式。所有这些结果都用于求解多元极大熵插值问题。本文给出了非交换（或交换）解析Toeplitz代数F_n^ \infty（或W_n^\infty）及其与B（H，K）的张量积的Sarason，Caratheodory-Schur和Nevanlinna-Pick型插值问题的极大熵解（及其熵）的显式表达式.特别地，我们给出了C^n的单位球上的几个插值（或优化）问题的极大熵解的显式形式。
Curvature, Dolbeault-Dirac operators, and an $\mathrm{L}^p$-index theorem on compact Kähler manifolds
本文在紧Kähler流形上建立了Dolbeault-Dirac算子的$\mathrm{L}^p$-Banach非交换几何框架，证明了其闭实现是双扇形的且具有有界$\mathrm{H}^\infty$泛函演算，并得到$\mathrm{L}^p$-Hodge分解和Fredholm算子的指标等于全纯Euler示性数。
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