A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules

Let H be a Hilbert C*-module over a matrix algebra A. It is proved that any function T:H --> H which preserves the absolute value of the (generalized) inner product is of the form Tf=Phi(f )Uf (f is an element of H), where Ph i is a phase-function and U is an A-linear isometry. The result gives a nat ural extension of Wigner's classical unitary-antiunitary theorem for Hilber t modules. (C) 1999 American Institute of Physics. [S0022- 2488(99)01611-4] .