Intersection theory and the Horn inequalities for invariant subspaces
We provide a direct, intersection theoretic, argument that the Jordan models of an operator of class Co, of its restriction to an invariant subspace, and of its compression to the orthogonal complement, satisfy a multiplicative form of the Horn inequalities, where 'inequality' is replaced...
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| Dokumentumtípus: | Cikk |
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Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 1-2 |
| Kulcsszavak: | Invariáns alterek, Horn egyenlőtlenségek, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-015-538-z |
| Online Access: | http://acta.bibl.u-szeged.hu/46450 |
| Tartalmi kivonat: | We provide a direct, intersection theoretic, argument that the Jordan models of an operator of class Co, of its restriction to an invariant subspace, and of its compression to the orthogonal complement, satisfy a multiplicative form of the Horn inequalities, where 'inequality' is replaced by 'divisibility'. When one of these inequalities is saturated, we show that there exists a splitting of the operator into quasidirect summands which induces similar splittings for the restriction of the operator to the given invariant subspace and its compression to the orthogonal complement. The result is true even for operators acting on nonseparable Hilbert spaces. For such operators the usual Horn inequalities are supplemented so as to apply to all the Jordan blocks in the model. |
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| Terjedelem/Fizikai jellemzők: | 235-269 |
| ISSN: | 0001-6969 |