Thompson-type formulae

الأصل · EN

Let X and Y be two nxn Hermitian matrices. In the article "Proof of a conjectured exponential formula" (Linear and Multilinear Algebra (19) 1986, 187-197) R. C. Thompson proved that there exist two nxn unitary matrices U and V such that eⁱ ˣeⁱ ʸ=ei (UXU*+VBV*). In this note we consider extensions of this result to compact operators as well as to operators in an embeddable II₁ factor.