Nonlinear preservers problem of complex symmetric operators

Abstract

Given a conjugation [Formula: see text] on a separable complex Hilbert space [Formula: see text], a bounded linear operator [Formula: see text] on [Formula: see text] is said to be [Formula: see text]-symmetric if [Formula: see text]. In this paper, we study some nonlinear preserving problems concerning [Formula: see text]-symmetric operators and diagonal operators, as a result, we also describe those nonlinear preservers of the lattice of invariant subspaces.