On the geometry of normal projections in Krein spaces
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 compo...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2015 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/17759 |
| Online Access: | http://hdl.handle.net/11336/17759 |
| Access Level: | Open access |
| Keyword: | Normal operator Projection Krein space Submanifold https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | 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↦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. |
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