Bijective bounded module morphisms preserving all norm-closed submodules on full Hilbert A-modules are exactly the multiplications by invertible elements of the center of the multiplier algebra.
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C*-submodule preserving module mappings on Hilbert C*-modules
Bijective bounded module morphisms preserving all norm-closed submodules on full Hilbert A-modules are exactly the multiplications by invertible elements of the center of the multiplier algebra.