A+ CATEGORY SCIENTIFIC UNIT

Linear preservers of equivalence relations on infinite-dimensional spaces

Volume 238 / 2017

Tatjana Petek, Gordana Radić Studia Mathematica 238 (2017), 101-119 MSC: Primary 47B49; Secondary 15A86. DOI: 10.4064/sm8356-12-2016 Published online: 28 April 2017

Abstract

Linear maps preserving equivalence, equivalence by unitaries or congruence, acting on an infinite-dimensional Banach/Hilbert space, are classified. In the first two cases a unified approach is used: we identify the orbit of the identity and show that it is invariant under the map under consideration. Known results on linear invertibility or unitary group preservers are then used.

Authors

  • Tatjana PetekFaculty of Electrical Engineering and
    Computer Science
    University of Maribor
    Smetanova ul. 17
    SI-2000 Maribor, Slovenia
    and
    Institute of Mathematics, Physics and Mechanics
    Jadranska ul. 19
    SI-1000 Ljubljana, Slovenia
    e-mail
  • Gordana RadićFaculty of Electrical Engineering and
    Computer Science
    University of Maribor
    Smetanova ul. 17
    SI-2000 Maribor, Slovenia
    e-mail

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