Sums of three quadratic endomorphisms of an infinite-dimensional vector space
Let V be an infinite-dimensional vector space over a field. In a previous article [5], we have shown tha t every endomorphism of V splits into the sum of four square-zero ones but also into the sum of four idempotent ones. Here, we study decompositions into sums of three endomorphisms with prescribe...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2017
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| Sorozat: | Acta scientiarum mathematicarum
83 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-016-319- 1 |
| Online Access: | http://acta.bibl.u-szeged.hu/48918 |
| Tartalmi kivonat: | Let V be an infinite-dimensional vector space over a field. In a previous article [5], we have shown tha t every endomorphism of V splits into the sum of four square-zero ones but also into the sum of four idempotent ones. Here, we study decompositions into sums of three endomorphisms with prescribed split annihilating polynomials with degree 2. Except for endomorphisms tha t are the sum of a scalar multiple of the identity and of a finite-rank endomorphism, we achieve a simple characterization of such sums. In particular, we give a simple characterization of the endomorphisms tha t split into the sum of three square-zero ones, and we prove tha t every endomorphism of V is a linear combination of three idempotents. |
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| Terjedelem/Fizikai jellemzők: | 83-111 |
| ISSN: | 0001 6969 |