Related papers: The Cowen-Douglas Theory for Operator Tuples and S…
We consider a subclass of the Cowen-Douglas class in which the problem of deciding whether two operators are similar becomes more manageable. A similarity criterion for Cowen-Douglas operators is known to be dependent on the trace of the…
In this paper, a new criterion for the similarity of commuting tuples of operators on Hilbert spaces is introduced. As an application, we obtain a geometric similarity invariant of tuples in the Cowen-Douglas class which gives a partial…
A curvature inequality is established for contractive commuting tuples of operators in the Cowen-Douglas class of rank n. Properties of the extremal operators, that is, the operators which achieve equality, are investigated. Specifically, a…
The study of Cowen-Douglas operators not only involves traditional operator-theoretic tools but also concepts and results from complex geometry on holomorphic vector bundles. We make use of the ratio of the metric matrices first considered…
In 1978, M. J. Cowen and R.G. Douglas introduce a class of operators (known as Cowen-Douglas class of operators) and associates a Hermitian holomorphic vector bundle to such an operator in a very influential paper. They give a complete set…
The study of Cowen-Douglas operators involves not only operator-theoretic tools but also complex geometry on holomorphic vector bundles. By leveraging the properties of holomorphic vector bundles, this paper investigates the cyclicity of…
We show that the same similarity characterization obtained for Cowen-Douglas operators to the backward shift operators on reproducing kernel Hilbert spaces with analytic kernels can be used to describe similarity in the Dirichlet space…
In this paper we study quasi-homogeneous operators, which include the homogeneous operators, in the Cowen-Douglas class. We give two separate theorems describing canonical models (with respect to equivalence under unitary and invertible…
The curvature $\mathcal K_T(w)$ of a contraction $T$ in the Cowen-Douglas class $B_1(\mathbb D)$ is bounded above by the curvature $\mathcal K_{S^*}(w)$ of the backward shift operator. However, in general, an operator satisfying the…
The classical Cowen-Douglas class of (commuting tuples of) operators possessing an open set of (joint) eigenvalues of finite constant multiplicity was introduced by Cowen and Douglas, generalizing the backward shifts. Their unitary…
Fix a bounded planar domain $\Omega.$ If an operator $T,$ in the Cowen-Douglas class $B_1(\Omega),$ admits the compact set $\bar{\Omega}$ as a spectral set, then the curvature inequality $\mathcal K_T(w) \leq - 4 \pi^2 S_\Omega(w,w)^2,$…
In 1978, M. J. Cowen and R. G. Douglas introduced a class of geometric operators (known as Cowen-Douglas class of operators) and associated a Hermitian holomorphic vector bundle to such operators. In this paper, after giving some basic…
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…
For an operator $T$ in the class ${\mathrm B}_n(\Omega)$, introduced in \cite{CD}, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle $E_T$ determine…
We establish a connection between the de Branges-Rovnyak spaces and the Cowen-Douglas class of operators which is associated with complex geometric structures. We prove that the backward shift operator on a de Branges-Rovnyak space never…
Denote $\mathcal{FB}_{n}(\Omega)$ as the collection of operators possessing a flag structure in the Cowen-Douglas class $\mathcal{B}_{n}(\Omega)$, and all the irreducible homogeneous operators in $\mathcal{B}_{n}(\Omega)$ belong to this…
We introduce a set of operator-valued invariants for localization of operator tuples in the Cowen-Douglas class, with which a Specht-type criterion for unitary equivalence is obtained.
The explicit description of irreducible homogeneous operators in the Cowen-Douglas class and the localization of Hilbert modules naturally leads to the definition of a smaller class of Cowen-Douglas operators possessing a flag structure.…
In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated with sets of noncommutative polynomials. We obtain analogues of classical results…
In this note, we will define the formulas of curvature and it's covariant derivatives for holomorphic curves on C*-algebras for the multivariable case. As applications, the unitarily and similarly classification theorems for holomorphic…