gap topologies on adjointable module maps

Suppose w is a hilbert c*-module and r(w) is the set of all unbounded regular operators between w.suppose b_{1}(w) denotes the set of all bounded adjointable operators t on w of norm |t | leq 1. we equip the sets with gap topologies and show that the adjoint preserving bijection r(w) to { f in b(w):| f|leq 1 , {rm and} range(1- f^* f ) {rm is} {rmdense} {rm in} w } , t mapsto t(1+t^*t)^{-1/2} is bicontinuous. we can use this fact to occasionally think of r(w) as being a subspace of the closed unit ball of b(w).