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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Uniqueness of zero-functional extension holds for Hilbert C*-module pairs over W*-algebras, monotone complete C*-algebras, compact C*-algebras, and one-sided maximal modular ideals of any C*-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.
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Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals
Uniqueness of zero-functional extension holds for Hilbert C*-module pairs over W*-algebras, monotone complete C*-algebras, compact C*-algebras, and one-sided maximal modular ideals of any C*-algebra.