A note on the star order in Hilbert spaces

J. Antezana, C. Cano, I. Mosconi, D. Stojanoff

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31 Citations (Scopus)


We study the star order on the algebra L(H) of bounded operators on a Hilbert space H. We present a new interpretation of this order which allows to generalize to this setting many known results for matrices: functional calculus, semi-lattice properties, shorted operators and orthogonal decompositions. We also show several properties for general Hilbert spaces regarding the star order and its relationship with the functional calculus and the polar decomposition, which were unknown even in the finitedimensional setting. We also study the existence of strong limits of starmonotone sequences and nets. © 2010 Taylor & Francis.
Original languageEnglish
Pages (from-to)1037-1051
JournalLinear and Multilinear Algebra
Issue number8
Publication statusPublished - 1 Nov 2010


  • Functional calculus
  • Polar decomposition
  • Projections
  • Semi-lattice structure
  • Shorted operators
  • Star order


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