Related papers: Cowen-Douglas operators and analytic continuation

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…

We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator…

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…

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras. In particular, we give several applications of operator space theory, based on the surprising fact that certain maps are…

In this paper, two related types of dualities are investigated. The first is the duality between left-invertible operators and the second is the duality between Banach spaces of vector-valued analytic functions. We will examine a pair…

In this paper we show a Cowen-Douglas operator $T \in \mathcal{B}_{n}(\Omega)$ is the adjoint operator of some backward shift on a general basis by choosing nice cross-sections of its complex bundle $E_{T}$. Using the basis theory model, we…

In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory…

Let T be a Cowen-Douglas tuple on a Banach space X. We use functional representations of T to associate with each T-invariant subspace Y of X an integer called the fiber dimension of Y. Among other results we prove a limit formula for the…

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…

We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…

We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…

We use elementary algebraic properties of left, right multiplication operators to prove some deep structural properties of left $m$-invertible, $m$-isometric, $m$-selfadjoint and other related classes of Banach space operators, often adding…

Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of…

In Bergman and Dirichlet spaces, the shift operator is not an isometry, but it is a left invertible operator. In this paper we give conditions on the left invertible operators such that a operator version, in the sense of Rosenblum and…

We construct some inverse-closed algebras of bounded integral operators with operator-valued kernels, acting in spaces of vector-valued functions on locally compact groups. To this end we make systematic use of covariance algebras…

We study the Moore-Penrose inverse of perturbations by a symmetrically-normed ideal of a closed range operator on a Hilbert space. We show that the notion of essential codimension of projections gives a characterization of subsets of such…

Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*-algebras. The primary object of this paper is the norm-closed operator algebra generated by a left…

Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…

We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…

Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (\alpha_j -A)^{-1}$ are given. Several examples are considered.