Thompson-type formulae

Abstract

Let X and Y be two n×n Hermitian matrices. In the article Proof of a conjectured exponential formula (Linear Multilinear Algebra 19 (1986) 187-197) R.C. Thompson proved that there exist two n×n unitary matrices U and V such thateiXeiY=eiUXU*+VYV*. In this note we consider extensions of this result to compact operators as well as to operators in an embeddable II 1 factor.