Abstract.
Under the mild condition of continuity at a single point we describe all the bijections of the set of all partial isometries on a Hilbert space which preserve the order and the orthogonality in both directions. Moreover, we present a natural analogue of Wigner's theorem on quantum mechanical symmetries for the set of all rank-1 partial isometries.
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Eingegangen am 31. 3. 2000
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Molnár, L. On certain automorphisms of sets of partial isometries. Arch. Math. 78, 43–50 (2002). https://doi.org/10.1007/s00013-002-8215-3
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DOI: https://doi.org/10.1007/s00013-002-8215-3