Extracting square roots of Bergmann operators (Q5955996)

In [Manuscr. Math. 101, 351-360 (2000; Zbl 0981.32012)], \textit{W. Kaup} and \textit{J. Sauter} used deep results on \(JB^*\)-triples (the Gelfand-Naimark-Friedmann-Russo Theorem) to show that the positive square root of the Bergmann operator \(B(x,\overline{x})\), where \(x\) runs in a bounded symmetric domain \(\mathcal D\) determined by a \(JB^*\)-triple, can be extended continuously to the boundary of \(\mathcal D\). In the paper under review, an elementary proof of this fact is given based only on the binomial series. This method does not require holomorphic or continuous functional calculus, it yields explicit formulas for \(B(x,\overline{x})^{1/2}\), and it is applicable to real bounded symmetric domains as well.