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

Lajos Molnar

doi:10.1063/1.533044

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arXiv · math/9909049

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

Lajos Molnar

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Abstract

Let H be a Hilbert $C^*$-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 $Tf=ϕ(f)Uf$ $(f\in H)$, 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.

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BibTeX RIS

Lajos Molnar. 1999-09-09. A generalization of Wigner's unitary-antiunitary theorem to Hilbert modules. https://doi.org/10.1063/1.533044

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