Descriptions of partial isometries on Hilbert C∗-modules

Partial isometries and Moore–Penrose inverses of bounded adjointable operators on Hilbert C∗-modules are investigated. It is shown that a contraction between Hilbert C∗-modules is a partial isometry if and only if it possesses a contractive Moore–Penrose inverse. A bounded adjointable operator T is a partial isometry if and only if its bounded transform is 2-1/2T.