Related papers: On the Berger-Coburn phenomenon

It is proposed that instead of normal representations one should look at cocycles of group extensions valued in certain groups of unitary operators acting in a Hilbert space (e.g the Fock space of chiral fermions), when dealing with groups…

In this paper, we study the product of a Hankel operator and a Toeplitz operator on the Hardy space. We give necessary and sufficient conditions of when such a product $H_f T_g$ is compact.

The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…

A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal…

We characterize all pairs of entire functions $(u,\psi)$ for which the induced weighted superposition operator $S_{(u,\psi)}$ transforms one Fock space into another Fock space.Further analytical structures like boundedness and Lipschitz…

For $E$ a Hilbert space, let $\mathcal{H}(E)$ denote the Segal-Bargmann space (also known as the Fock space) over $E$, which is a reproducing kernel Hilbert space with kernel $K(x,y)=\exp(< x,y>)$ for $x,y$ in $E$. If $\phi$ is a mapping on…

In the classical Hardy space $H^2(\mathbb{D})$, it is well-known that the kernel of the Hankel operator is invariant under the action of shift operator S and sometimes nearly invariant under the action of backward shift operator $S^{*}$. It…

We prove the $K$-theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and $C^*$-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes…

Let $\mu$ be a positive Borel measure on the interval [0,1). For $\alpha>0$, the Hankel matrix $\mathcal{H}_{\mu,\alpha}=(\mu_{n,k,\alpha})_{n,k\geq 0}$ with entries…

We characterise the Schatten class $S^p$ properties of commutators $[b,T]$ of singular integrals and pointwise multipliers in a general framework of (quasi-)metric measure spaces. This covers, unifies, and extends a range of previous…

The main purpose of this paper is to study the generalized Hilbert operator {equation*} \mathcal{H}_g(f)(z)=\int_0^1f(t)g'(tz)\,dt {equation*} acting on the weighted Bergman space $A^p_\om$, where the weight function $\om$ belongs to the…

The usual examples of Bergman spaces consist of the closure of an algebra of holomorphic functions on a domain. One can also take the real part of such functions, but essentially one is looking at the same object. In this paper the author…

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces $H^\Psi$: construction of a "slow" Blaschke product giving a non-compact composition operator on $H^\Psi$;…

We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes $S_p$ of the Hardy space $\mathcal{H}^2$ of Dirichlet series. For $p\geq 2$, these conditions lead to a…

The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence,…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^n$ with Lipschitz boundary and $\phi$ be a continuous function on $\overline{\Omega}$. We show that the Toeplitz operator $T_{\phi}$ with symbol $\phi$ is compact on the weighted…

This paper uses frame techniques to characterize the Schatten class properties of integral operators. The main result shows that if the coefficients of certain frame expansions of the kernel of an integral operator are in (\ell^{2,p}), then…

Let f:E-->B be a fibration of fiber F. Eilenberg and Moore have proved that there is a natural isomorphism of vector spaces between H^*(F;F_p) and Tor^{C^*(B)}(C^*(E),F_p). Generalizing the rational case proved by Sullivan, Anick [Hopf…

This paper is concerned with paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space. By considering when such operators commute, generalizations of the Brown--Halmos results for…

We develop an operator-theoretic approach to quaternionic Fock spaces, with emphasis on Carleson measures, Berezin transforms, and Toeplitz operators. We first introduce a global Gaussian $L^p$-framework on $\mathbb H$ for slice functions…