A Generalization of Wigner’s Unitary-antiunitary Theorem to Hilbert Modules
نویسنده
چکیده
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 = φ(f)Uf (f ∈ H), where φ is a phase-function and U is an A-linear isometry. The result gives a natural extension of Wigner’s classical unitary-antiunitary theorem for Hilbert modules. 1991 Physics and Astronomy Classification Scheme (PACS): 02.30.Sa; 02.30.Tb. 1 2 WIGNER’S UNITARY-ANTIUNITARY THEOREM FOR MODULES
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