Related papers: Holomorphic operator valued functions generated by…

The class of operator-valued functions which are homogeneous of degree one, holomorphic in the open right polyhalfplane, have positive semidefinite real parts there and take selfadjoint operator values at real points, and its subclass…

Contractive selfadjoint extensions of a Hermitian contraction $B$ in a Hilbert space ${\mathfrak H}$ with an exit in some larger Hilbert space ${\mathfrak H}\oplus{\mathcal H}$ are investigated. This leads to a new geometric approach for…

We generalize our earlier results from \cite{K} on the Bessmertny\u{\i} class of operator-valued functions holomorphic in the open right poly-halfplane which admit representation as a Schur complement of a block of a linear homogeneous…

We characterize the zero sets of functions in the Schur--Agler class over the unit polydisk as well as functions in the unit ball of the multiplier algebra of the Drury--Arveson space via operators associated with a unitary realization…

The operator-valued Schur-class is defined to be the set of holomorphic functions $S$ mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator…

In this paper we extend the $H^\infty$ functional calculus to quaternionic operators and to $n$-tuples of noncommuting operators using the theory of slice hyperholomorphic functions and the associated functional calculus, called…

We give a new characterization of the class ${\bf N}^0_{\mathfrak M}[-1,1]$ of the operator-valued in the Hilbert space ${\mathfrak M}$ Nevanlinna functions that admit representations as compressed resolvents ($m$-functions) of selfadjoint…

Let $E$ be a $W^{\ast}$-correspondence over a von Neumann algebra $M$ and let $H^{\infty}(E)$ be the associated Hardy algebra. If $\sigma$ is a faithful normal representation of $M$ on a Hilbert space $H$, then one may form the dual…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

We study here class of 1D spectral-meromorphic (s-meromorphic) OD operators $L=\partial_x^n+\sum_{n-2\geq i\geq 0}a_{n-2-i}\partial_x^i$ with meromorphic coefficients $a_j$ near $x\in R$ such that all eigenfunctions $L\psi=\alpha\psi$ are…

Given a complex, separable Hilbert space $\mathcal{H}$, we consider self-adjoint $L^2$-realizations of differential expressions $\tau = - (d^2/dx^2) I_{\mathcal{H}} + V(x)$, on half-lines and on the real line (assuming the limit-point…

The Schur class, denoted by $\mathcal{S}(\mathbb{D})$, is the set of all functions analytic and bounded by one in modulus in the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$, that is \[ \mathcal{S}(\mathbb{D}) = \{\varphi…

Let $\mathfrak M$ and $\mathfrak N$ be separable Hilbert spaces and let $\Theta(\lambda)$ be a function from the Schur class ${\bf S}(\mathfrak M,\mathfrak N)$ of contractive functions holomorphic on the unit disk. The operator…

We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward…

Let $H_m(\mathbb B,\mathcal D)$ be the $\mathcal D$-valued functional Hilbert space with reproducing kernel $K_m(z,w) = (1-\langle z,w\rangle)^{-m}1_{\mathcal D}$. A $K_m$-inner function is by definition an operator-valued analytic function…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

If $z\mapsto a_z$ is a holomorphic function with values in the sectorial forms in a Hilbert space, then the associated operator valued function $z\mapsto A_z$ is resolvent holomorphic. We give a proof of this result of Kato, on the basis of…

Let $U$ be an operator in a Hilbert space $\mathcal{H}_{0}$, and let $\mathcal{K}\subset\mathcal{H}_{0}$ be a closed and invariant subspace. Suppose there is a period-2 unitary operator $J$ in $\mathcal{H}_{0}$ such that $JUJ=U^*$, and $PJP…

Passive systems $\tau={T,M,N,H}$ with $M$ and $N$ as an input and output space and $H$ as a state space are considered in the case that the main operator on the state space is normal. Basic properties are given and a general unitary…

Let $\mathcal G$ be a Hilbert space and $\mathfrak B(\mathcal G)$ the algebra of bounded operators, $\mathcal H=L_2([0,\infty);\mathcal G)$. An operator-valued function $Q\in L_{\infty,\rm loc}\left([0,\infty);\mathfrak B(\mathcal…