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Wigner's theorem in Hilbert |
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| Authors: | Damir Bakic Boris Guljas |
| Institution: | Department of Mathematics, University of Zagreb, Bijenicka c. 30, 10000 Zagreb, Croatia ; Department of Mathematics, University of Zagreb, Bijenicka c. 30, 10000 Zagreb, Croatia |
| Abstract: | Let  be a Hilbert  -module over the  -algebra  of all compact operators on a Hilbert space. It is proved that any function  which preserves the absolute value of the  -valued inner product is of the form  , where  is a phase function and  is an  -linear isometry. The result generalizes Molnár's extension of Wigner's classical unitary-antiunitary theorem. |
| Keywords: | $C^*$-algebra Hilbert $C^*$-module compact operator Wigner's theorem |
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