Normal projections in Krein spaces

ALEJANDRA MAESTRIPIERI; FRANCISCO MARTÍNEZ PERÍA

INTEGRAL EQUATIONS AND OPERATOR THEORY

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2013 vol. 76 p. 357 - 380

0378-620X

Given a complex Krein space $HH$ with fundamental symmetry $J$, the aim of this note is to characterize the set of $J$-normal projections [ Q={Qin L(HH): Q^2=Q ext{and} Q^#Q=QQ^#}. ] The ranges of the projections in $Q$ are exactly those subspaces of $HH$ which are pseudo-regular. For a fixed pseudo-regular subspace $St$, there are infinitely many $J$-normal projections onto it, unless $St$ is regular. Therefore, most of the material herein is devoted to parametrizing the set of $J$-normal projections onto a fixed pseudo-regular subspace $St$.