Related papers: Hilbert space operators with two-isometric dilatio…

We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ if and only if the norms of its powers grow polynomially. In analogy with unitary dilations of contractions, we prove that such…

Quasi-isometric liftings similar to isometries, for the operators similar to contractions in Hilbert spaces, are investigated. The existence of such liftings is established, and their applications are explored for specific operator classes,…

We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal.…

In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our…

An operator T on Hilbert space is a 3-isometry if there exists operators B and D such that (T*)^n T^n = I+nB +n^2 D. An operator J is a Jordan operator if it the sum of a unitary U and nilpotent N of order two which commute. If T is a…

Let $(S_1, S_2)$ be a bi-isometry, that is, a pair of commuting isometries $S_1$ and $S_2$ on a complex Hilbert space $\mathscr H.$ By the von Neumann-Wold decomposition, the hyper-range $\mathscr H_\infty(S_1):=\cap_{n=0}^\infty…

Let $\mathcal{H}$ be a complex Hilbert space and let $\big\{A_{n}\big\}_{n\geq 1}$ be a sequence of bounded linear operators on $\mathcal{H}$. Then a bounded operator $B$ on a Hilbert space $\mathcal{K} \supseteq \mathcal{H}$ is said to be…

In this paper, we give the Alzer inequality for Hilbert space operators as follows: Let $A, B$ be two selfadjoint operators on a Hilbert space $\mathcal H$ such that $0 < A, B \le \frac{1}{2}I$, where $I$ is identity operator on $\mathcal…

Given a row contraction of operators on Hilbert space and a family of projections on the space which stabilize the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries which satisfy natural…

A classical result of Sz.-Nagy asserts that a Hilbert-space contraction operator $T$ can be lifted to an isometry $V$. A more general multivariable setting of recent interest for these ideas is the case where (i) the unit disk is replaced…

The aim of this paper is to obtain $ m $-isometric dilation of expansive $ m $-concave operator on Hilbert space. The obtained dilation is shown to be minimal. The matrix representation of this dilation is given. It is also proved that in…

This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…

A commuting triple of Hilbert space operators $(A,S,P)$ is said to be a \textit{$\mathbb{P}$-contraction} if the closed pentablock $\overline{\mathbb P}$ is a spectral set for $(A,S,P)$, where \[ \mathbb{P}:=\left\{(a_{21}, \mbox{tr}(A_0),…

A commuting pair of operators (S, P) on a Hilbert space H is said to be a Gamma-contraction if the symmetrized bidisc is a spectral set of the tuple (S, P). In this paper we develop some operator theory inspired by Agler and Young's results…

In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted composition operators on the Hilbert space $L^2(\mu)$. Also, we find that normal-$m$-isometry and normal quasi-$m$-isometry weighted composition operators have…

We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…

Let $A$ be a positive bounded linear operator on a complex Hilbert space $\mathcal{H}$ and $\mathcal{B}_{A}(\mathcal{H})$ be the subspace of all operators which admit $A$-adjoints operators. In this paper, we establish some inequalities…

A Hilbert space operator $S\in\B$ is left $m$-invertible by $T\in\B$ if $$\sum_{j=0}^m{(-1)^{m-j}\left(\begin{array}{clcr}m\\j\end{array}\right)T^jS^j}=0,$$ $S$ is $m$-isometric if…

We investigate $\rho$-orthogonality and its local symmetry in the space of bounded linear operators. A characterization of Hilbert space operators with symmetric numerical range is established in terms of $\rho$-orthogonality. Further, we…

It is shown that a pair of Hilbert space operators V and W such that V*W=I (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal basis are replaced with biorthogonal sequences, and it is also…