Related papers: Operator Theory on Symmetrized Bidisc

We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function…

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…

Given a contraction A on a Hilbert space H, an operator T on H is said to be A-invariant if <Tx,x>=<TAx,Ax> for every x in H such that ||Ax||=||x||. In the special case in which both defect indices of A are equal to 1, we show that every…

For $0<r<1$, let us consider the following annulus: \[ \mathbb A_r= \{ z\in \mathbb C\, : \, r<|z|<1 \}. \] A Hilbert space operator $T$ for which $\overline{\mathbb A}_r$ is a spectral set is called an $\mathbb A_r$-\textit{contraction}.…

Using works of T.~Ando and L.~Gurvits, the well-known theorem of P.R.~Halmos concerning the existence of unitary dilations for contractive linear operators acting on Hilbert spaces recast as a result for $d$-tuples of contractive Hilbert…

In this paper we present a result which establishes a connection between the theory of compact operators and the theory of iterated function systems. For a Banach space X, S and T bounded linear operators from X to X such that \parallel S…

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…

We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…

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…

Sz.-Nagy and Foias proved that each $C_{\cdot0}$-contraction has a dilation to a Hardy shift and thus established an elegant analytic functional model for contractions of class $C_{\cdot0}$. This has motivated lots of further works on model…

The goal of the present paper is to push Sz.-Nagy--Foias model theory for a completely nonunitary Hilbert-space contraction operator $T$, to the case of a commuting pair of contraction operators $(T_1, T_2)$ having product $T = T_1 T_2$…

The article deals with isometric dilation and commutant lifting for a class of $n$-tuples $(n \geq 3)$ of commuting contractions. We show that operator tuples in the class dilate to tuples of commuting isometries of BCL type. As a…

A commuting tuple of Hilbert space operators $(T_1, \dotsc, T_n)$ is said to be an \textit{$\mathbb{A}_r^n$-contraction} if the closure of the polyannulus \[ \mathbb A_r^n=\left\{(z_1, \dotsc, z_n) \ : \ r<|z_i|<1, \ 1 \leq i \leq n…

We develop a Clark theory for commuting compressed shift operators on model spaces $K_{\phi}$ associated with inner functions $\phi$ on the bidisk, which exhibits both similarities and marked differences compared to the classical…

The hexablock is a domain arising from a special case of the $\mu$-synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is called a hexablock-contraction or simply $\mathbb…

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…

Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…

An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is…

The closed symmetrized tridisc $\Gamma_3$ and its distinguished boundary $b\Gamma_3$ are the sets $\Gamma_3=\{ (z_1+z_2+z_3,z_1z_2+z_2z_3+z_3z_1,z_1z_2z_3): \,|z_i|\leq 1, i=1,2,3 \}\subseteq \mathbb C^3$ $b\Gamma_3=\{…

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…