Generic Properties of Module Maps and Characterizing Inverse Limits of C*-Algebras of Compact Operators

We study closedness of the range, adjointability and generalized invertibility of modular operators between Hilbert modules over locally C*-algebras of coefficients. Our investigations and the recent results of M. Frank reveal a number of equivalence properties of the category of Hilbert modules over locally C*-algebras which characterize precisely the inverse limit of C*-algebras of the C*-algebra of compact operators.