33 research outputs found
Operator theory and function theory in Drury-Arveson space and its quotients
The Drury-Arveson space , also known as symmetric Fock space or the
-shift space, is a Hilbert function space that has a natural -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.Comment: Final version (to appear in Handbook of Operator Theory); 42 page
Perturbations of nuclear C*-algebras
Kadison and Kastler introduced a natural metric on the collection of all
C*-subalgebras of the bounded operators on a separable Hilbert space. They
conjectured that sufficiently close algebras are unitarily conjugate. We
establish this conjecture when one algebra is separable and nuclear. We also
consider one-sided versions of these notions, and we obtain embeddings from
certain near inclusions involving separable nuclear C*-algebras. At the end of
the paper we demonstrate how our methods lead to improved characterisations of
some of the types of algebras that are of current interest in the
classification programme.Comment: 45 page