Optimal normal projections in Krein spaces

Abstract

Given a pseudo-regular subspace S of a Krein space H with fundamental symmetry J, if its isotropic part S◦ is not trivial the set QS of J-normal projections onto S has infinitely many elements. The aim of this work is to distinguish a projection Q0 ∈ QS according to a suitable criterion. When H is finitedimensional, Q0 turns out to be the unique minimal norm projection in QS with respect to the Schatten p-norm for 1 ≤ p < ∞.