Extracting square roots of Bergmann operators
In a recent preprint (No. 45 on this server), W. Kaup and
J. Sauter use the Gelfand-Naimark-Friedmann-Russo Theorem for
JB*-triples to show that the positive square root of the
Bergmann operator B(x,x), where x runs in a bounded symmetric
domain D determined by a JB*-triple, can be extended
continuously to the boundary of D. The purpose of this note is to
give an elementary proof of this fact, based only on the binomial
series. Our method does not require holomorphic or continuous functional
calculus, it yields explicit formulas for the square root, and it is
applicable to real bounded symmetric domains as well.
O. Loos <ottmar.loos@uibk.ac.at>