Geodesic
Operational quantities derived from the norm and generalized Fredholm theory
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 645-657 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We introduce and study some operational quantities associated to a space ideal $\Bbb A$. These quantities are used to define generalized semi-Fredholm operators associated to $\Bbb A$, and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that the classes of generalized semi-Fredholm operators are non-trivial for several classical space ideals.
We introduce and study some operational quantities associated to a space ideal $\Bbb A$. These quantities are used to define generalized semi-Fredholm operators associated to $\Bbb A$, and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that the classes of generalized semi-Fredholm operators are non-trivial for several classical space ideals.
Classification : 46B28, 47A30, 47A53, 47B10
Keywords: semi-Fredholm operator; strictly singular operator; perturbation 
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Gonzalez, Manuel; Martinon, Antonio. Operational quantities derived from the norm and generalized Fredholm theory. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 645-657. http://geodesic.mathdoc.fr/item/CMUC_1991_32_4_a6/

[1] Alvarez J.A., Alvarez T., Gonzalez M.: The gap between subspaces and perturbation of non semi-Fredholm operators. Bull. Austral. Math. Soc., to appear. | MR | Zbl

[2] Alvarez T., Gonzalez M.: Some examples of tauberian operators. Proc. Amer. Math. Soc. 111 (1991), 1023-1027. | MR

[3] Alvarez T., Gonzalez M., Onieva V.M.: Totally incomparable Banach spaces and three-space Banach space ideals. Math. Nachrichten 131 (1987), 83-88. | MR | Zbl

[4] Alvarez T., Gonzalez M., Onieva V.M.: Characterizing two classes of operator ideals. Contribuciones Matematicas Homenaje Prof. Plans, Univ. Zaragoza (1990), 7-21.

[5] Fajnshtejn A.S.: On measures of noncompactness of linear operators and analogs of the minimal modulus for semi-Fredholm operators (in Russian). Spektr. Teor. Oper. 6 (1985), 182-185, Zbl. 634#47010.

[6] Goldberg S.: Unbounded Linear Operators. McGraw Hill, 1966. | MR | Zbl

[7] Gonzalez M., Martinon A.: Operational quantities and operator ideals. XIV Jornadas Hispano Lusas de Mat. (Univ. La Laguna, 1989), Univ. La Laguna, 1990, 119-124. | MR

[8] Gonzalez M., Martinon A.: A generalization of semi-Fredholm operators. preprint. | MR

[9] Gonzalez M., Onieva V.M.: On incomparability of Banach spaces. Math. Z. 192 (1986), 581-585. | MR | Zbl

[10] Gonzalez M., Onieva V.M.: Characterizations of tauberian operators. Proc. Amer. Math. Soc. 108 (1990), 399-405. | MR | Zbl

[11] Kadets M.I.: Note on the gap between subspaces. Funct. Anal. Appl. 9 (1975), 156-157. | Zbl

[12] Kalton N.J., Wilansky A.: Tauberian operators in Banach spaces. Proc. Amer. Math. Soc. 57 (1976), 233-240. | MR

[13] Kato T.: Perturbation theory for linear operators. Springer-Verlag, 1980. | Zbl

[14] Martinon A.: Cantidades operacionales en teoría de Fredholm (Thesis). Univ. La Laguna, 1989. | MR

[15] Pietsch A.: Operator ideals. North-Holland, 1980. | MR | Zbl

[16] Rosenthal H.P.: On totally incomparable Banach spaces. J. Funct. Anal. 4 (1969), 167-175. | MR | Zbl

[17] Schechter M.: Quantities related to strictly singular operators. Indiana Univ. Math. J. 21 (1972), 1061-1071. | MR | Zbl

[18] Sedaev A.A.: The structure of certain linear operators (in Russian). Mat. Issled. 5 (1970), 166-175, MR 43#2540, Zbl. 247#47005. | MR

[19] Stephani I.: Operator ideals generalizing the ideal of strictly singular operators. Math. Nachrichten 94 (1980), 29-41. | MR | Zbl

[20] Weis L.: Über striktly singuläre und striktly cosinguläre Operatoren in Banachräumen (Dissertation). Univ. Bonn, 1974.

[21] Zemánek J.: Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour. Studia Math. 80 (1984), 219-234. | MR