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semi1.tex~
\documentclass{article} \usepackage{amsfonts} \usepackage{amsmath} \begin{document} \section{Commutative models} Let $T_t$, $t\ge0$ be a centered semigroup. First we assume that the operators $T_t$ are invertible, i.e., have zero kernel and their image is the whole $H$. Write the polar decomposition, $T_t = U_tC_t$, then $C_t$ have (possibly unbounded) inverse, and $U_t$ are unitaries. \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End:
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