Thompson-type formulae

Abstract

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