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The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.
The corona problem was motivated by the question of the density of the open unit disk D in the maximal ideal space of the algebra, H1(D), of bounded holomorphic functions on D. In this note we study relationships of the problem with questions in oper
This paper is devoted to the study of reducing subspaces for multiplication operator $M_phi$ on the Dirichlet space with symbol of finite Blaschke product. The reducing subspaces of $M_phi$ on the Dirichlet space and Bergman space are related. Our st
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n times n$ matrices analogous to the classical Pick matrix. We study for which reproducing kernel Hilbert spaces it suffices to consider matrices of boun
We study vector-valued Littlewood-Paley-Stein theory for semigroups of regular contractions ${T_t}_{t>0}$ on $L_p(Omega)$ for a fixed $1<p<infty$. We prove that if a Banach space $X$ is of martingale cotype $q$, then there is a constant $C$ such that