Maps preserving the local spectrum of quadratic products of matrices
Let Mn(C) denote the algebra of all n × n complex matrices, and fix a nonzero vector x0 in C n . For any matrix T ∈ Mn(C), let σT (x0) denote the local spectrum of T at x0. Given three scalars µ, ν and ξ simultaneously nonzero, we study maps ϕ on Mn(C) satisfying σµST S+νT S+ξST (x0) = σµϕ(S)ϕ(T )ϕ(...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2018
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| Sorozat: | Acta scientiarum mathematicarum
84 No. 1-2 |
| Kulcsszavak: | Mátrixelmélet, Leképezés |
| Online Access: | http://acta.bibl.u-szeged.hu/55803 |
| Tartalmi kivonat: | Let Mn(C) denote the algebra of all n × n complex matrices, and fix a nonzero vector x0 in C n . For any matrix T ∈ Mn(C), let σT (x0) denote the local spectrum of T at x0. Given three scalars µ, ν and ξ simultaneously nonzero, we study maps ϕ on Mn(C) satisfying σµST S+νT S+ξST (x0) = σµϕ(S)ϕ(T )ϕ(S)+νϕ(T )ϕ(S)+ξϕ(S)ϕ(T )(x0) for all S, T ∈ Mn(C). Our main result extends and unifies the main results of several papers on maps on Mn(C) preserving the local spectrum of different products. |
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| Terjedelem/Fizikai jellemzők: | 49-64 |
| ISSN: | 0001-6969 |