An Interpolation Problem For Conjugations

Let H be a complex Hilbert space. We give a solution to the following interpolation problem: Characterize the class of pairs (M, N) of subspaces of H such that there is a conjugation C on H satisfying C(M) = N. We show that two subspaces M, N having this property simply means that they are in symmetric position, in the sense that dim(M boolean AND N-perpendicular to) = dim(M-perpendicular to boolean AND N). We present some of its applications to the study of complex symmetric operators and their relatives. (C) 2021 Elsevier Inc. All rights reserved.