Thompson-type formulae

JORGE ANTEZANA; GABRIEL LAROTONDA; ALEJANDRO VARELA

JOURNAL OF FUNCTIONAL ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2012 vol. 262 p. 1515 - 1528

0022-1236

Let $X$ and $Y$ be two $n imes n$ Hermitian matrices. In the article extit{Proof of a conjectured exponential formula} (Linear and Multilinear Algebra (19) 1986, 187-197)  R. C. Thompson proved that there exist two $n imes n$ 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.