Related papers: The Agler-Young Class
We give an alternative proof to Agler's famous result on success of rational dilation on an annulus by an application of a result due to Dritschel and McCullough. We show interplay between operators associated with an annulus, $C_{1,r}$ or…
In this note we quantize the free $ * $-algebra generated by finitely many variables, which is a new example of the theory of Toeplitz quantization of $ * $-algebras as developed previously by the author. This is achieved by defining…
The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces $\mathcal{H}_K$ on the unit ball in $\mathbb…
We establish upper bounds for the convolution operator acting between interpolation spaces. This will provide several examples of Young Inequalities in different families of function spaces. We use this result to prove a bilinear…
Let $G$ be a finite pseudoreflection group and $\Omega\subseteq \mathbb C^d$ be a bounded domain which is a $G$-space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of $\Omega$ and $\Omega/G$ using…
We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of…
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…
In this paper we introduce and study several new Hilbert-type operators acting between the weighted Fock spaces. We provide some sufficient and necessary conditions for the boundedness and compactness of certain Hilbert-type operators from…
We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. The central issue is to understand the connection…
We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a…
Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…
We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…
We prove several results concerning the theory of Toeplitz algebras over $p$-Fock spaces using a correspondence theory of translation invariant symbol and operator spaces. The most notable results are: The full Toeplitz algebra is the norm…
In studying commutants of analytic Toeplitz operators, Thomson proved a remarkable theorem which states that under a mild condition, the commutant of an analytic Toeplitz operator is equal to that of Toeplitz operator defined by a finite…
In this paper, we completely characterize when two dual truncated Toeplitz operators are essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Our main idea is to study dual truncated…
We study the class of Uglov bipartitions and prove a generalization of a conjecture by Dipper, James and Murphy. We give two consequences concerning the computation of canonical bases in affine type A and the description of decomposition…
We diagonalize the Hilbert space of some subclass of the quasifinite module of the \Winf algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of…
Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann's Cayley transform. Based on ideas of Woronowicz, we redevelop this theory from the point of view of…
We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the…
Based on the success of a well-known method for solving higher order linear differential equations, a study of two of the most important mathematical features of that method, viz. the null spaces and commutativity of the product of…