Decomposition of selfadjoint projections in Krein spaces

A. MAESTRIPIERI; F. MARTÍNEZ PERÍA

Guanajuato, México

Workshop; IWOTA 2009; 2009

A bounded operator $T$ is $B$-selfadjoint if it is selfadjoint respect to this sesquilinear form. We study the set $\mc{P}(B,\St)$ of $B$-selfadjoint projections with range $\St$, where $\St$ is a closed subspace of $\HH$. We state several conditions which characterize the existence of $B$-selfadjoint projections with a given range; among them certain decompositions of $\HH$, $R(|B|)$ and $R(|B|^{1/2})$. We also show that every $B$-selfadjoint projection can be factorized as the product of a $B$-contractive, a $B$-expansive and a $B$-isometric projection. Finally two different formulas for $B$-selfadjoint  projections are given.