CONTINUITY OF THE POLAR DECOMPOSITION FOR UNBOUNDED OPERATORS ON HILBERT C*-MODULES

For unbounded operators t, s between Hilbert C*-modules which admit the polar decompositions V vertical bar t vertical bar, W vertical bar s vertical bar, respectively, we obtain an explicit upper bound estimate for the gap between t and s in terms of the norm of the bounded operators V - W, C-vertical bar t vertical bar - C-vertical bar s vertical bar and C-vertical bar t*vertical bar - C-vertical bar s*vertical bar, where C-vertical bar t vertical bar and C-vertical bar s vertical bar are the Cayley transforms of vertical bar t vertical bar and vertical bar s vertical bar. The result are used to drive a criterion for continuity of the polar decomposition for unbounded operators between Hilbert C*-modules.