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Maps preserving the local spectrum of quadratic products of matrices.
- Source :
-
Acta Scientiarum Mathematicarum . Jun2018, Vol. 84 Issue 1/2, p49-64. 16p. - Publication Year :
- 2018
-
Abstract
- Let Mn(C) denote the algebra of all n × n complex matrices, and fix a nonzero vector x0 in Cn. 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 σμSTS+νTS+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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00016969
- Volume :
- 84
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Acta Scientiarum Mathematicarum
- Publication Type :
- Academic Journal
- Accession number :
- 154555058
- Full Text :
- https://doi.org/10.14232/actasm-017-590-0