Idempotents in a space with conjugation

Abstract

Let H be a complex Hilbert space with conjugation operator J. We study J-real operators and we have covered J-regular subspaces. We prove that for given bounded idempotent p there exists a conjugation operator J0 such that p is a J0-projection, i.e. p= J0p J0. © 2012 Elsevier Inc. All rights reserved.