Related papers: A note on $k$-hyperreflexivity of Toeplitz-harmoni…

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…

We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of…

We study reflexivity and structure properties of operator algebras generated by representations of the discrete Heisenberg semi-group. We show that the left regular representation of this semi-group gives rise to a semi-simple reflexive…

Let $\mathfrak A$ be a maximal subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$. If every right invariant subspace of $\mathfrak A$ in the non-commutative Hardy space $H^2$ is of Beurling type, then we say…

In this paper, we consider the relation between Toeplitz operators and elements in von Neumann algebras generated by certain graph groupoids.

Recently, M. Daws introduced a notion of co-representation of abelian Hopf--von Neumann algebras on general reflexive Banach spaces. In this note, we show that this notion cannot be extended beyond subhomogeneous Hopf--von Neumann algebras.…

The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to…

In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on…

We use a theorem by Gonzalez, Leon-Saavedra and Montes-Rodriguez to construct a class of coanalytic Toeplitz operators which have an infinite-dimensional closed subspace, where any non-zero vector is hypercyclic.

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

In this paper we study the product of Toeplitz operators on the harmonic Bergman space of the unit disk of the complex plane C. Mainly, we discuss when the product of two quasihomogeneous Toeplitz operators is also a Toeplitz operator, and…

We generalize recent results of Fleeman and Liaw on the topic of hyponormal Toeplitz operators acting on the Bergman space of the unit disk.

We consider a tensor product of two spaces of holomorphic functions on a Hermitian symmetric space of tube type. Then generically this is decomposed into a direct sum of irreducible subrepresentations. In this manuscript, we construct the…

The subspaces and subalgebras of B(H) which are hyperreflexive with constant 1 are completely classified. It is shown that there are 1-hyperreflexive subspaces for which the complete hyperreflexivity constant is strictly greater than 1. The…

We discuss the reflexivity of hyperexpansions and their Cauchy dual operators. In particular, we show that any cyclic completely hyperexpansive operator is reflexive. We also establish the reflexivity of the Cauchy dual of an arbitrary…

Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as K\"ahler and hyperbolic…

We investigate algebraic and topological transitivity and, more generally, k-transitivity for linear spaces of operators. In finite dimensions, we determine minimal dimensions of k-transitive spaces for every k, and find relations between…

We study Schur-type upper triangular forms for elements, T, of von Neumann algebras equipped with faithful, normal, tracial states. These were introduced in a paper of Dykema, Sukochev and Zanin; they are based on Haagerup-Schultz…

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the row operator $(V_1,...,V_n) : H^n \to H$ is an isometry. We prove that every isometric $n$-tuple is hyperreflexive, in the sense of…

For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…