Thompson-type formulae

2011/07/02 by Antezana, Jorge, Larotonda, Gabriel, Varela, Alejandro
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1107.0348

Abstract

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 e^{i X}e^{i Y}=e^{i (UXU^*+VBV^*)}. In this note we consider extensions of this result to compact operators as well as to operators in an embeddable II₁ factor.

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