Abstract Let S=(S 1,…, S d) denote the compression of the d-shift to the complement of a
homogeneous ideal I of C [z 1,…, zd]. Arveson conjectured that S is essentially normal. In …

We study operator algebras arising from monomial ideals in the ring of polynomials in
noncommuting variables, through the apparatus of subproduct systems and C …

We study subproduct systems in the sense of Shalit and Solel arising from stochastic
matrices on countable state spaces, and their associated operator algebras. We focus on the …

We continue the study of isomorphisms of tensor algebras associated to $ C^* $-
correspondences in the sense of Muhly and Solel. Inspired by recent work of Davidson …

We introduce and study two-parameter subproduct and product systems of C⁎-algebras as
the operator-algebraic analogues of, and in relation to, Tsirelson's two-parameter product …

We revisit tensor algebras of subproduct systems with Hilbert space fibers, resolving some
open questions in the case of infinite-dimensional fibers. We characterize when a tensor …

In this thesis we bring together several techniques in the theory of non-self-adjoint operator
algebras and operator systems. We begin with classification of non-self-adjoint and self …