Identificador persistente para citar o vincular este elemento:
http://hdl.handle.net/10662/15823
Títulos: | Linear maps preserving the generalized spectrum |
Autores/as: | Mbekhta, Mostafa |
Palabras clave: | Módulo mínimo reducido;Espectro generalizado;Isomorfismo de Jordan;Problemas de conservación líneal;Reduced minimum modulus;Generalized spectrum;Jordan isomorphism;Linear preserver problems |
Fecha de publicación: | 2007 |
Editor/a: | Universidad de Extremadura, Servicio de Publicaciones |
Resumen: | Let 𝐻 be an infinite-dimensional separable complex Hilbert space and 𝛣 (𝐻) the algebra of all bounded linear operators on 𝐻. For an operator 𝑇 in 𝛣(𝐻), let σɡ(𝑇) denote the generalized spectrum of T. In this paper, we prove that if ø: 𝛣(𝐻) → 𝛣(𝐻) is a surjective linear map, then ø preserves the generalized spectrum (i.e. øɡ(ø (𝑇)) = ø (𝑇) for every 𝑇 ∊ 𝛣(𝐻)) if and only if there is A ∊ 𝛣(𝐻) invertible such that either ø(𝑇) = A𝑇A‾¹ for every 𝑇 ∊𝛣(𝐻), or ø(𝑇) = A𝑇trA‾¹ for every 𝑇 ∊ 𝛣(H). Also, we prove that γ(ø(𝑇)) = γ(𝑇) for every 𝑇 ∊ 𝛣(𝐻) if and only if there is U ∊ 𝛣(𝐻) unitary such that either ø(𝑇) = U𝑇U* for every 𝑇 ∊ 𝛣(𝐻) or ø(𝑇) = U𝑇trU¤ for every 𝑇 ∊ 𝛣(𝐻ɡ). Here γ(𝑇) is the reduced minimum modulus of 𝑇. |
URI: | http://hdl.handle.net/10662/15823 |
ISSN: | 0213-8743 |
Colección: | Extracta Mathematicae Vol. 22, nº 1 (2007) |
Archivos
Archivo | Descripción | Tamaño | Formato | |
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2605-5686_22_1_45.pdf | 163,34 kB | Adobe PDF | Descargar |
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