Linear preservers of equivalence relations on infinite-dimensional spaces
Volume 238 / 2017
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.
