Related papers: A Note on Tetrablock Contractions

We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix…

We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…

For a diagonalizable linear operator $H:\mathscr{H}\to\mathscr{H}$ acting in a separable Hilbert space $\mathscr{H}$, i.e., an operator with a purely point spectrum, eigenvalues with finite algebraic multiplicities, and a set of…

We establish some operator versions of Bellman's inequality. In particular, we prove that if $\Phi: \mathbb{B}(\mathscr{H}) \to \mathbb{B}(\mathscr{K})$ is a unital positive linear map, $A,B \in \mathbb{B}(\mathscr{H})$ are contractions,…

We give a self-contained and introductory account of some basic functional analytic tools needed to understand maximal monotone operators in Hilbert spaces. We review domains of (possibly unbounded) operators, closed sets and closed…

The set \[ \overline{\mathbb{E}}= \{ x \in {\mathbb{C}}^3: \quad 1-x_1 z - x_2 w + x_3 zw \neq 0 \mbox{ whenever } |z| < 1, |w| < 1 \} \] is called the tetrablock and has intriguing complex-geometric properties. It is polynomially convex,…

A fundamental theorem of Sz.-Nagy states that a contraction $T$ on a Hilbert space can be dilated to an isometry $V.$ A more multivariable context of recent significance for these concepts involves substituting the unit disk with…

In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…

We prove sufficient conditions for Hausdorff convergence of the spectra of sequences of closed operators defined on varying Hilbert spaces and converging in norm-resolvent sense, i.e. $\|J_\varepsilon(1+A_\varepsilon)^{-1} -…

The Hilbert transform is essentially the \textit{only} singular operator in one dimension. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on…

There are three main results in this paper. First, we find an easily computable and simple condition which is necessary and sufficient for a commuting tuple of contractions to possess a non-zero Toeplitz operator. This condition is just…

Consider a finite dimensional complex Hilbert space $\cH$, with $dim(\cH) \geq 3$, define $\bS(\cH):= \{x\in \cH \:|\: ||x||=1\}$, and let $\nu_\cH$ be the unique regular Borel positive measure invariant under the action of the unitary…

Let $D,X \in B(H)$ be bounded operators on an infinite dimensional Hilbert space $H$. If the commutator $[D,X] = DX-XD$ lies within $\varepsilon$ in operator norm of the identity operator $1_{B(H)}$, then it was observed by Popa that one…

We study the interaction between unitary $\rho$-dilations of a pair of Hilbert space operators and Birkhoff-James orthogonality. We prove that for two orthogonal operators $T,A$ if $\|T\|=\rho$, then $U_T \perp_B U_A$ for any unitary…

Vertex operators, being families of birational transformations of infinite-dimensional algebraic ``varieties'' M, act on appropriate line bundles on M. However, they act on (meromorphic) sections only as_partial operators_: they are defined…

Let $H$ be a complex separable Hilbert space and $B(H)$ the algebra of all bounded linear operators on $H$. In this paper, we give considerable generalizations of the inequalities for norms of commutators of normal operators. Let $S, T \in…

It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted…

We study a family of lattice Schr\"odinger operators $H_{\mu_1\mu_2}(K)$ describing two identical bosons on the three-dimensional cubic lattice $\mathbb{Z}^3$, where $K \in \mathbb{T}^3$ is the quasi-momentum, and $\mu_1, \mu_2 \in…

We present a spectral triple for $\kappa$-Minkowski space in two dimensions. Starting from an algebra naturally associated to this space, a Hilbert space is built using a weight which is invariant under the $\kappa$-Poincar\'e algebra. The…