hyperbolic isomorphism
Let be a Banach space and a continuous linear isomorphism. We say that is an hyperbolic isomorphism if its spectrum is disjoint with the unit circle, i.e. .
If this is the case, by the spectral theorem there is a splitting of into two invariant subspaces, (and therefore, a corresponding splitting of into two operators and , i.e. ), such that and . Also, for any greater than the spectral radius of both and there exists an equivalent (box-type) norm such that
and
In particular, can be chosen smaller than , so that and are contractions.
Title | hyperbolic isomorphism |
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Canonical name | HyperbolicIsomorphism |
Date of creation | 2013-03-22 13:39:34 |
Last modified on | 2013-03-22 13:39:34 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 10 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 37D05 |
Classification | msc 46B03 |
Synonym | linear hyperbolic isomorphism |