In this volume we study noncommutative domains $\mathcal {D} _f\subset B (\mathcal {H})^
n $ generated by positive regular free holomorphic functions $ f $ on $ B (\mathcal {H})^ n …

Let B (H) be the algebra of all bounded linear operators on a Hilbert space H. The main goal
of the paper is to find large classes of noncommutative domains in B (H) with prescribed …

This concise monograph explores how core ideas in Hardy space function theory and
operator theory continue to be useful and informative in new settings, leading to new …

We characterize operator-valued Bergman inner functions on the unit ball as functions
admitting a suitable transfer function realization. Thus we extend corresponding one …

This paper is an attempt to unify the multivariable operator model theory for ball-like
domains and commutative polydiscs and extend it to a more general class of …

A pair of commuting operators (S, P) defined on a Hilbert space 𝓗 for which the closed
symmetrized bidisc Γ=(z1+ z2, z1z2):| z1|≤ 1,| z2|≤ 1⊆ ℂ2 is a spectral set is called a Γ …

Abstract Let Q ⊂ C\left< Z_1, ..., Z_n\right> Q⊂ CZ 1,…, Z n be an arbitrary set of
polynomials in noncommutative indeterminates such that q (0)= 0 q (0)= 0 for all q ∈ Q q∈ …

Let Q be a set of polynomials in noncommutative indeterminates Z i, j, i∈{1,…, k}, j∈{1,…,
ni}. In this paper, we study noncommutative varieties VQ (H):={X={X i, j}∈ D (H): g (X)= 0 for …

We introduce and study a Fock-space noncommutative analogue of reproducing kernel
Hilbert spaces of de Branges-Rovnyak type. Results include: use of the de Branges …

An interesting and recently much studied generalization of the classical Schur class is the
class of contractive operator-valued multipliers for the reproducing kernel Hilbert space H …