Mathematics – Functional Analysis
Scientific paper
2011-07-02
Mathematics
Functional Analysis
Scientific paper
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.
Antezana Jorge
Larotonda Gabriel
Varela Alejandro
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