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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Referencias
P. Aiena,
textit{Fredholm and Local Spectral Theory, with Application to Multipliers}, Kluwer Acad. Publishers (2004).
P. Aiena,
{it Quasi-Fredholm operators and localized SVEP}. Acta Sci. Mat. (Szeged) {bf 73} (2007), 251-263.
P. Aiena, M. T. Biondi and C. Carpintero, {it On Drazin invertibility},
Proc. Amer. Math. Soc. {bf 136} (2008), 2839-2848.
F. Astudillo-Villalba and J. Ramos-Fern'{a}ndez {it Multiplication operators on the space of functions of bounded variation}, Demonstr. Math. {bf 50}(1) (2017), 105-115.
B. Barnes, {it The spectral and Fredholm theory of extensions of bounded linear operators}, Proc. Amer. Math. Soc. {bf 105}(4) (1989), 941-949.
B. Barnes, {it Restrictions of bounded linear operators: closed range}, Proc. Amer. Math. Soc. {bf 135}(6) (2007), 1735-1740.
M. Berkani, {it Restriction of an operator to the range of its powers}, Studia Math. {bf 140}(2) (2000), 163-175.
M. Berkani, {it On a class of quasi-Fredholm operators}, Int. Equa. Oper. Theory {bf 34} (1) (1999), 244-249.
M. Berkani and M. Sarih, {it On semi B-Fredholm operators}, Glasgow Math. J. {bf 43} (2001), 457-465.
M. Berkani and H. Zariouh, {it Extended Weyl type theorems}, Math. Bohemica. {bf 134}(4) (2009), 369-378.
Berkani and J. Koliha, {it Weyl type theorems for bounded linear operators},
Acta Sci. Math. (Szeged) {bf 69} (2003), 359-376.
M. Berkani and H. Zariouh, {it New extended Weyl type theorems},
Mat. Vesnik. {bf 62} (2010), 145-154.
M. Berkani, M. Sarih and H. Zariouh, {it Browder-type theorems and SVEP},
Mediterr. J. Math. {bf 8} (2011), 399-409.
C. Carpintero, A. Guti'{e}rrez, E. Rosas, y J. Sanabria, {it A note on preservation of generalized Fredholm spectra in Berkani's sense}, Filomat. {bf 32}(18) (2018), 6431-6440.
C. Carpintero, A. Guti'{e}rrez, E. Rosas, y J. Sanabria, {it A note on preservation of spectra for two given operators}, to appear on Mathematica Bohemica. (2019).
C. Carpintero, A. Malaver, E. Rosas y J. Sanabria, {it On the hereditary character of new strong variations of Weyl type Theorems}, to appear on An. Stiint. Univ. Al. I. Cuza Iasi. Mat.(2019)
C. Carpintero, E. Rosas, O. Garc'{i}a y J. Sanabria, {it On the hereditary character of certain spectral properties and some applications}, submitted to Proyecciones Journal of Mathematics (2019).
L. A. Coburn, {it Weyl's Theorem for Nonnormal Operators},
Research Notes in Mathematics. {bf 51} (1981).
L. Chen and W. Su, {it A note on Weyl-type theorems and restrictions}, Ann. Funct. Anal. {bf 8(2)} (2017), 190-198.
J. K. Finch,
{it The single valued extension property on a Banach space},
Pacific J. Math. {bf 58} (1975), 61-69.
A. Gupta and K. Mamtani,
{it Weyl-type theorems for restrictions of closed linear unbounded operators},
Acta Univ. M. Belli Ser. Math. {bf 2015}, 72-79.
R. E. Harte and W. Y. Lee, {it Another note on Weyl's theorem},
Trans. Amer. Math. Soc. {bf 349} (1997), 2115-2124.
H. Heuser, textit{Functional Analysis}, Marcel Dekker, New York 1982.
E. Hewitt and K. Ross, textit{Abstract harmonic analysis I },
Springer-Verlag, Berlin 1963.
K. Jorgus, textit{Linear operators },
Pitman, Boston 1982.
V. Rakov{c}evi'{c},
{it Operators obeying $a$-Weyl's theorem},
Rev. Roumaine Math. Pures Appl. {bf 34}(10) (1989), 915-919.
V. Rakov{c}evi'{c}, {it On a class of operators},Math. Vesnick. {bf 37} (1985), 423-426.
J. Sanabria, C. Carpintero, E. Rosas and O. Garc'{i}a, {it On generalized property $(v)$ for bounded linear operators},
Studia Math. {bf 212} (2012), 141-154.
H. Zariouh, {it Property $(gz)$ for bounded linear operators}, Mat. Vesnik. {bf 65}(1) (2013), 94-103
bibitem{A2} H. Zariouh, {it New version of property $(az)$}, Mat. Vesnik. {bf 66}(3) (2014), 317-322
H. Weyl, {it Uber beschrankte quadratiche Formen, deren Differenz vollsteigist}, Rend. Circ. Mat. Palermo, {bf 27} (1909), 373-392.