Thompson-type formulae

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 that eiXeiY = eiUXU∗+VYV∗ . In this note we consider extensions of this result to compact operators as well as to operators in an embeddable II1 factor. © 2011 Elsevier Inc. All rights reserved.