Nonlinear maps preserving the pseudo spectral radius of skew semi-triple products of operators
Let H be a complex Hilbert space of dimension greater than 2, and denote by L(H) the algebra of all bounded linear operators on H. For ε > 0 and T ∈ L(H), let rε(T) denote the ε-pseudo spectral radius of T. Let S1 and S2 be subsets of L(H) which contain all rank one operators and the identity. A...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2018
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| Sorozat: | Acta scientiarum mathematicarum
84 No. 1-2 |
| Kulcsszavak: | Leképezés, Operátorelmélet |
| Online Access: | http://acta.bibl.u-szeged.hu/55802 |
| Tartalmi kivonat: | Let H be a complex Hilbert space of dimension greater than 2, and denote by L(H) the algebra of all bounded linear operators on H. For ε > 0 and T ∈ L(H), let rε(T) denote the ε-pseudo spectral radius of T. Let S1 and S2 be subsets of L(H) which contain all rank one operators and the identity. A characterization is obtained for surjective maps φ: S1 → S2 satisfying rε(φ(T)φ(S) ∗φ(T)) = rε(T S∗T) (T, S ∈ S1). An analogous description is also obtained for the pseudo spectrum of operators. |
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| Terjedelem/Fizikai jellemzők: | 39-47 |
| ISSN: | 0001-6969 |