On maps preserving operators of local spectral radius zero
| Autor: | A. Jaatit, M. Elhodaibi |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Numerical Analysis Algebra and Number Theory Spectral radius 010102 general mathematics Linear operators Zero (complex analysis) Banach space 010103 numerical & computational mathematics 01 natural sciences Surjective function Bounded function Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Algebra over a field Mathematics |
| Zdroj: | Linear Algebra and its Applications. 512:191-201 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2016.10.001 |
| Popis: | Let L ( X ) be the algebra of all bounded linear operators on a complex Banach space X. We describe surjective linear maps ϕ on L ( X ) that satisfy r ϕ ( T ) ( x ) = 0 ⟹ r T ( x ) = 0 for every x ∈ X and T ∈ L ( X ) . We also describe surjective linear maps ϕ on L ( X ) that satisfy r T ( x ) = 0 ⟹ r ϕ ( T ) ( x ) = 0 for every x ∈ X and T ∈ L ( X ) . Furthermore, we characterize maps ϕ (not necessarily linear nor surjective) on L ( X ) which satisfy r ϕ ( T ) − ϕ ( S ) ( x ) = 0 if and only if r T − S ( x ) = 0 for every x ∈ X and T , S ∈ L ( X ) . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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