This paper belongs to a recent spate of papers (see, for example, [Linear Algebra Appl. 431, No. 5–7, 833–842 (2009; Zbl 1183.47031); ibid., 974–984 (2009; Zbl 1183.15017)] in the same issue as the paper being reviewed, and references therein). The common thread of these papers is to characterize maps on Hilbert space satisfying a certain property (preservers), without assuming linearity. For instance, in the paper under review, the following is proven:
Given an infinite-dimensional Hilbert space , let , and let , such that
, with , or
, with invertible and conjugate linear.