On certain automorphisms of sets of partial isometries

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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.

Original languageEnglish
Pages (from-to)43-50
Number of pages8
JournalArchiv der Mathematik
Volume78
Issue number1
DOIs
Publication statusPublished - Jan 1 2002

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ASJC Scopus subject areas

  • Mathematics(all)

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