IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
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.