IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
On the geometry of normal projections in Krein spaces
Autor/es:
EDUARDO CHIUMIENTO; FRANCISCO MARTÍNEZ PERÍA; ALEJANDRA MAESTRIPIERI
Revista:
JOURNAL OF OPERATOR THEORY
Editorial:
THETA FOUNDATION
Referencias:
Lugar: Bucharest; Año: 2015 vol. 74 p. 101 - 101
ISSN:
0379-4024
Resumen:
Let $\h$ be a Krein space with fundamental symmetry $J$. Along this paper, the geometric structure of the set of $J$-normal projections $\q$ is studied. The group of $J$-unitary operators $\uj$ naturally acts on $\q$. Each orbit of this action turns out to be an analytic homogeneous space of $\uj$, and a connected component of $\q$. The relationship between $\q$ and the set $\e$ of $J$-selfadjoint projections is analized: both sets are analytic submanifolds of $L(\h)$ and there is a natural real analytic submersion from $\q$ onto $\e$, namely $Q\mapsto QQ^\#$.The range of a $J$-normal projection is always a pseudo-regular subspace. Then, for a fixed pseudo-regular subspace $\s$, it is proved that the set of $J$-normal projections onto $\s$ is a covering space of the subset of $J$-normal projections onto $\s$ with fixed regular part.