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 that e i X e i Y = e i U X U ⁎ + V Y V ⁎ . In this note we consider extensions of this result to compact operators as well as to operators in an embeddable II 1 factor.
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