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arXiv · 1107.0348

Thompson-type formulae

Jorge Antezana·Gabriel Larotonda·Alejandro Varela
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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 II$_1$ factor.

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Jorge Antezana, Gabriel Larotonda, Alejandro Varela. 2011-07-02. Thompson-type formulae. https://arxiv.org/abs/1107.0348

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