Normal projections in Krein spaces

FRANCISCO MARTÍNEZ PERÍA

Biograd na Moru

Conferencia; The Third Najman Conference on Spectral Problems for Operators and Matrices; 2013

Departments of Mathematics of TU Chemnitz and Univeristy of Zagreb

The aim of this talk is to present some results on (bounded), normal projections acting on Krein spaces, that is those projections acting on a Krein space that commute with their adjoints with respect to the indefinite inner product. Although every normal projection acting on a Hilbert space turns out to be selfadjoint, this is not the case on Krein spaces. Indeed, a (closed) subspace is the range of a normal projection if and only if it is pseudo-regular, i.e. the direct sum of its isotropic part and a regular subspace. We are going to discuss different characterizations of normal projections and a parametrization for the set of normal projections onto a (fixed) pseudo-regular subspace. This talk is based on a joint work with A. Maestripieri.