Michael T. Jury

Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators

We prove that the norm of a weighted composition operator on the Hardy space H 2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space as- sociated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H 2 , and recover the standard upper bound for the norm. Sim- ilar arguments apply to weighted Bergman spaces. We also show that the positivity of a generalized de Branges-Rovnyak kernel is sufficient for the boundedness of a given composition operator on the standard functions spaces on the unit ball.

Composition operators on Hardy spaces of a half-plane

We prove that a composition operator is bounded on the Hardy space

Nevanlinna–Pick interpolation on distinguished varieties in the bidisk

H^2

Partially isometric dilations of noncommuting N-tuples of operators

of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative

Aleksandrov–Clark Theory for Drury–Arveson Space

\lambda

Invariant subspaces for a class of complete Pick kernels

there. In this case the norm, essential norm, and spectral radius of the operator are all equal to

IDEAL STRUCTURE IN FREE SEMIGROUPOID ALGEBRAS FROM DIRECTED GRAPHS

\sqrt{\lambda}

The Fredholm Index for Elements of Toeplitz-Composition C*-Algebras

.

C -ALGEBRAS GENERATED BY GROUPS OF COMPOSITION OPERATORS

Abstract This article treats Nevanlinna–Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.

Norms and spectral radii of linear fractional composition operators on the ball

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.