Related papers: Transitivity and bundle shifts

Consider a Hilbert space obtained as the completion of the polynomials C[z} in m-variables for which the mnonomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same…

An operator $T$ acting on a separable complex Hilbert space $H$ is said to be hypercyclic if there exists $f\in H$ such that the orbit $\{T^n f:\ n\in \mathbb{N}\}$ is dense in $H$. Godefroy and Shapiro \cite{GoSha} characterized those…

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…

It is shown that the algebra \(L^\infty(\mu)\) of all bounded measurable functions with respect to a finite measure \(\mu\) is localizing on the Hilbert space \(L^2(\mu)\) if and only if the measure \(\mu\) has an atom. Next, it is shown…

We consider an action of a compact group whose dual is archimedean linearly ordered or a direct product (or sum) of such groups on a von Neumann algebra, M. We define the generalized Hardy subspace of the Hilbert space of a standard…

We consider an action of the circle group, T on a von Neumann algebra, M. Similarly to the case when the algebra of essentially bounded functions on T is acted upon by translations, we define the generalized Hardy subspace of H,where H is…

Let $E$ be a $W^{\ast}$-correspondence over a von Neumann algebra $M$ and let $H^{\infty}(E)$ be the associated Hardy algebra. If $\sigma$ is a faithful normal representation of $M$ on a Hilbert space $H$, then one may form the dual…

We continue an analysis of representations of cylindrical functions and fluxes which are commonly used as elementary variables of Loop Quantum Gravity. We consider an arbitrary principal bundle of a compact connected structure group and…

We study analytic models of operators of class $C_{\cdot 0}$ with natural positivity assumptions. In particular, we prove that for an $m$-hypercontraction $T \in C_{\cdot 0}$ on a Hilbert space $\mathcal{H}$, there exists a Hilbert space…

For any given bounded symmetric domain, we prove the existence of commutative $C^*$-algebras generated by Toeplitz operators acting on any weighted Bergman space. The symbols of the Toeplitz operators that generate such algebras are defined…

The Hardy space on the unit ball in C^n provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n=1 the submodule has finite codimension. In this note…

We apply the ADM approach to obtain a Hamiltonian description of the Einstein-Hilbert action. In doing so we add four new ingredients: (i) We eliminate the diffeomorphism constraints. (ii) We replace the densities $\sqrt g$ by a function…

Following upon results of Putinar, Sun, Wang, Zheng and the first author, we provide models for the restrictions of the multiplication by a finite Balschke product on the Bergman space in the unit disc to its reducing subspaces. The models…

An algebra A of operators on a Banach space X is called strictly semi-transitive if for all non-zero x,y in X there exists an operator S in A such that Sx=y or Sy=x. We show that if A is norm-closed and strictly semi-transitive, then every…

Let $\mathbb H$ be the finite direct sums of $H^2(\mathbb D)$. In this paper, we give a characterization of the closed subspaces of $\mathbb H$ which are invariant under the shift, thus obtaining a concrete Beurling-type theorem for the…

Hausel introduced a commutative algebra -- the multiplicity algebra -- associated to a fixed point of the C^*-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector…

We here construct an explicit isomorphism between any commutative Hopf algebra which underlying coalgebra is the tensor coalgebra of a space $V$ and the shuffle algebra based on the same space. This isomorphism uses the commutative…

This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…

Let $\M$ be a finite von Neumann algebra acting on a Hilbert space $\H$ and $\AA$ be a transitive algebra containing $\M'$. In this paper we prove that if $\AA$ is 2-fold transitive, then $\AA$ is strongly dense in $\B(\H)$. This implies…

Starting with a Lie algebroid ${\cal A}$ over a space $M$ we lift its action to the canonical transformations on the affine bundle ${\cal R}$ over the cotangent bundle $T^*M$. Such lifts are classified by the first cohomology $H^1({\cal…