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

Abstract

Let H be a Hilbert $C^{\ast }$-module over a matrix algebra A. It is proved that any function $T:H\to H$ which preserves the absolute value of the (generalized) inner product is of the form $Tf=\varphi (f)Uf$ $(f\in H)$, where $\varphi$ 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.

arXiv comment27 pages. To appear in J. Math. Phys

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