The interpolation in CSL subalgebras of von Neumann algebras

摘要

Given a CSL subalgebra A of a von Neumann algebra and vectors f, g, we give necessary and sufficient conditions for the existence of an operator A epsilon A Of such that Af = g. This generalizes the corresponding results of Lance [5], Hopenwasser [2] and Katsoulis [4]. Furthermore, the necessary and sufficient conditions for multi-variable interpolation are described. (C) 2019 Elsevier Inc. All rights reserved.