Notas sobre propiedades espectrales de un operador, su heredabilidad y aplicaciones
Resumen
Este art\'{\i}culo versa sobre el comportamiento de los Teoremas, o propiedades, de tipo Weyl para un operador $T$ sobre un subespacio propio cerrado y $T$-invariante $W\subseteq X$ tal que $T^n(X)\subseteq W$, para alg\'{u}n $n\geq 1$, donde $T\in L(X)$ y $X$ es un espacio de Banach complejo e infinito dimensional. Nuestro principal prop\'{o}sito es exhibir que para tales subespacios (los cuales generalizan el caso $T^n(X)$ cerrado, para alg\'{u}n $n\geq 0$), una gran cantidad de Teoremas tipo Weyl se transmiten de $T$ a su restricci\'{o}n sobre $W$ y viceversa. Como aplicaci\'{o}n de nuestros resultados, obtenemos condiciones para que los Teoremas de tipo Weyl sean equivalentes para dos operadores dados. As\'{\i} como tambi\'{e}n, condiciones bajo las cuales un operador que act\'{u}a sobre un subespacio de un espacio dado, pueda extenderse a todo el espacio preserv\'{a}ndose las propiedades tipo Weyl.Visitas al artículo
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