Abstract. We prove that every bijective transformation on the set of Hilbert space effects which preserves a symmetric norm of a given Kubo--Ando mean is necessarily implemented by either a unitary or an antiunitary operator.

DOI: 10.14232/actasm-018-016-z

AMS Subject Classification (1991): 46L60, 47B49

Keyword(s): nonlinear preservers, Hilbert space effects, operator interval, Kubo--Ando mean, order automorphism, unitary operator

Received January 24, 2018 and in final form February 20, 2018. (Registered under 16/2018.)