  The second part of our work on operator synthesis deals with individual
operator synthesis of elements in some tensor products, in particular in
Varopoulos algebras, and its connection with linear operator equations. Using a
developed technique of ``approximate inverse intertwining'' we obtain some
generalizations of the Fuglede and the Fuglede-Weiss theorems. Additionally, we
give some applications to spectral synthesis in Varopoulos algebras and to
partial differential equations.

Functional Analysis;Operator Algebras