A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction
by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly …

We examine the semicrossed products of a semigroup action by∗-endomorphisms on a C*-
algebra, or more generally of an action on an arbitrary operator algebra by completely …

We study crossed products of arbitrary operator algebras by locally compact groups of
completely isometric automorphisms. We develop an abstract theory that allows for …

Semicrossed product algebras have been used to study dynamical systems since their
introduction by Arveson in 1967. In this survey article, we discuss the history and some …

We establish the isomorphism OX⋊ α r G≃ OX⋊ α r G for any non-degenerate-
correspondence and any discrete group acting on. In the case where is hyperrigid, a similar …

We study the Wold decomposition for representations of a self-similar semigroup P action on
a directed graph E. We then apply this decomposition to the case where P= N to study the C …

We take a new look at dilation theory for nonself-adjoint operator algebras. Among the
extremal (co) extensions of a representation, there is a special property of being fully …

Motivated by the theory of tensor algebras and multivariable $\mathrm {C}^* $-dynamics, we
revisit two fundamental techniques in the theory of $\mathrm {C}^* $-corres-pondences, the …

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

Since their inception in the 1930s by von Neumann, operator algebras have been used to
shed light on many mathematical theories. Classification results for self-adjoint and non-self …