Proceedings of the American Mathematical Society

Author(s): Damir Bakic; Boris Guljas
Journal: Proc. Amer. Math. Soc. 130 (2002), 2343-2349.
MSC (1991): Primary 46C05, 46C50; Secondary 39B42, 47J05
Posted: March 8, 2002
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Abstract: Let

be a Hilbert

-module over the

-algebra $\mathcal{A}\not = \boldsymbol{\mathit{C}}$ of all compact operators on a Hilbert space. It is proved that any function $T: W \rightarrow W$ which preserves the absolute value of the ${\mathcal A}$ -valued inner product is of the form $Tv=\varphi(v)Uv,\, v \in W$ , where $\varphi$ is a phase function and

is an ${\mathcal A}$ -linear isometry. The result generalizes Molnár's extension of Wigner's classical unitary-antiunitary theorem.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46C05, 46C50, 39B42, 47J05

Damir Bakic
Affiliation: Department of Mathematics, University of Zagreb, Bijenicka c. 30, 10000 Zagreb, Croatia
Email: bakic@math.hr

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