Related papers: Cowen-Douglas Operator and Shift on Basis

This paper is a sequel to our work in \cite{Das-Mundayadan}. Here, we primarily study the dynamics of the adjoint of a weighted forward shift operator $F_w$ on the analytic function space $\ell^p_{a,b}$ having a normalized Schauder basis of…

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 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.…

By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of Hill's method for numerical approximation of spectra of…

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…

Let $T$ be a bounded linear operator on a complex separable infinite dimensional Hilbert space $\mathcal{H}$. $T$ is called intransitive if it leaves invariant spaces other than 0 or the whole space $\mathcal{H}$; otherwise it is…

Consider a bounded strongly pseudo-convex domain $\Omega $ with a smooth boundary in $\mathbb{C}^n$. Let $\mathcal{T}$ be the Toeplitz algebra on the Bergman space $L^2_a(\Omega )$. That is, $\mathcal{T}$ is the $C^\ast $-algebra generated…

The explicit description of homogeneous operators and localization of a Hilbert module naturally leads to the definition of a class of Cowen-Douglas operators possessing a flag structure. These operators are irreducible. We show that the…

We introduce a new class which generalizes the class of B-Weyl operators. We say that $T\in L(X)$ is pseudo B-Weyl if $T=T_1\oplus T_2$ where $T_1$ is a Weyl operator and $T_2$ is a quasi-nilpotent operator. We show that the corresponding…

An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc $\mathbb D$ is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous…

A complete list of homogeneous operators in the Cowen-Douglas class $B_n(D)$ is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the…

Applying the techniques resulting the existence of almost invariant half-spaces, similarity models $\wh T$ can be given for upper triangular operator-matrices $T= \left[\begin{matrix}A&C\\ 0&B\end{matrix}\right]$. The model $\wh T$ is also…

In this article, we obtain two sets of results. The first set of complete results are exclusively for the case of the bi-disc while the second set of results describe in part, which of these carry over to the general case of the poly-disc:…

For a general Calderon-Zygmund operator $T$ on $R^N$, it is shown that $\|Tf\|_{L^2(w)}\leq C(T)\|w\|_{A_2}\|f\|_{L^2(w)}$ for all Muckenhoupt weights $w\in A_2$. This optimal estimate was known as the $A_2$ conjecture. A recent result of…

In this paper, we systematically study a class of essentially normal operators by using the geometry method from the Cowen-Douglas theory and prove a Brown-Douglas-Fillmore theorem in the Cowen-Douglas theory. More precisely, the Chern…

In this paper, we study the dynamics of an operator $\mathcal T$ naturally associated to the so-called Collatz map, which maps an integer $n \geq 0$ to $n / 2$ if $n$ is even and $3n + 1$ if $n$ is odd. This operator $\mathcal T$ is defined…

In resonance to a recent geometric framework proposed by Douglas and Yang, a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space is developed. By taking advantage of the refined…

Let $T^n$ denote the n-dimensional torus. The class of the bounded operators on $L^2(T^n)$ with analytic orbit under the action of $T^n$ by conjugation with the translation operators is shown to coincide with the class of the zero-order…

We investigate continuous linear operators, which commute with the generalized backward shift operator (a one-dimensional perturbation of the Pommiez operator) in a countable inductive limit $E$ of weighted Banach spaces of entire…

The noncommutative Choquet boundary and the C*-envelope of operator systems of the form Span{1,T,T*}, where T is a Hilbert space operator with normal-like features, are studied. Such operators include normal operators, k-normal operators,…