On Fuglede-Putnam properties

Abstract

In this paper, we study the Fuglede-Putnam property. We give a necessary and sufficient condition for which (circle plus(n)(i=1) A(i), circle plus B-n(i=1)i)satisfies the Fuglede-Putnam property. We also study the local spectral theory associated with the Fuglede-Putnam property. Finally, we define the weak Fuglede-Putnam property and we investigate several cases which satisfy the weak Fuglede-Putnam property.