Connections between Banach space theory and classical operator theory on Hilbert space
are multifold. First, one can generalize notions and results involving linear operators on a …

Contents Introduction Part I. Function theory 1. Basic properties of H 2 2. Multipliers and the
d-dimensional shift 3. von Neumann's inequality and the sup norm 4. Maximality of the H2 …

In this book the authors develop a theory of free noncommutative functions, in both algebraic
and analytic settings. Such functions are defined as mappings from square matrices of all …

Bohr's inequality says that if generators. We also include an application to Banach algebras.
We prove that every Banach algebra has an equivalent norm in which it satisfies a non …

We obtain an explicit representation formula and a Nevanlinna-Pick-type interpolation
theorem for the multiplier space of the reproducing kernel space ℌ (kd) of analytic functions …

Abstract In [6, 17, 18, 20], a good case is made that the appropriate analogue for the analytic
Toeplitz algebra in n non-commuting variables is the wot-closed algebra generated by the …

The seminal 1989 work of Douglas and Paulsen on the theory of analytic Hilbert modules
precipitated a number of major research efforts. This in turn led to some intriguing and …

The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the
left regular representation of the free semigroup on n generators. We obtain a distance …

We develop a theory of holomorphic functions in several noncommuting (free) variables and
provide a framework for the study of tuples of bounded linear operators on Hilbert spaces …

General results of interpolation (eg, Nevanlinna-Pick) by elements in the noncommutative
analytic Toeplitz algebra F∞(resp., noncommutative disc algebra A n) with consequences to …