Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
operational quantities; Fredholm theory
operational quantities; Fredholm theory
Summary:
In this paper we consider maps called operational quantities, which assign a non-negative real number to every operator acting between Banach spaces, and we obtain relations between the kernels of these operational quantities and the classes of operators of the Fredholm theory.
References:
[1] 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), 182-195.
[2] Galaz-Fontes F.: Measures of noncompactness and upper semi-Fredholm perturbation theorems. Proc. Amer. Math. Soc. 118 (1993), 891-897. MR 1151810 | Zbl 0782.47013
[3] Goldberg S.: Unbounded Linear Operators. McGraw-Hill, New York, 1966. MR 0200692 | Zbl 1152.47001
[4] González M., Martinón A.: Operational quantities derived from the norm and measures of noncompactness. Proc. R. Ir. Acad. 91 A (1991), 63-70. MR 1173159
[5] González M., Martinón A.: Operational quantities derived from the norm and generalized Fredholm theory. Comment. Math. Univ. Carolinae 32 (1991), 645-657. MR 1159811
[6] González M., Martinón A.: Fredholm theory and space ideals. Boll. U.M.I. 7 B (1993), 473-488. MR 1223653
[7] González M., Martinón A.: Note on operational quantities and the Mil'man isometry spectrum. Rev. Acad. Canar. Cienc. 3 (1991), 103-111. MR 1175602
[8] González M., Martinón A.: On incomparability of Banach spaces. in: Functional Analysis and Operator Theory, pp. 161-174, Banach Center Publications, vol. 30, Institute of Mathematics, Polish Academy of Sciences, Warzawa, 1994. MR 1285605
[9] González M., Martinón A.: Operational quantities characterizing the semi-Fredholm operators. Studia Math. 114 (1995), 13-27. MR 1330214
[10] Lebow A., Schechter M.: Semigroups of operators and measures of noncompactness. J. Funct. Anal. 7 (1971), 1-26. MR 0273422 | Zbl 0209.45002
[11] Martinón A.: Generating real maps on a biordered set. Comment. Math. Univ. Carolinae 32 (1991), 265-272. MR 1137787
[12] Pietsch A.: Operators Ideals. North-Holland, Amsterdam, 1980. MR 0582655
[13] Rakocevic V.: Measures of non-strict-singularity of operators. Mat. Vesnik 35 (1983), 79-82. MR 0724182 | Zbl 0532.47006
[14] Schechter M.: Quantities related to strictly singular operators. Indiana Univ. Math. J. 21 (1972), 1061-1071. MR 0295103 | Zbl 0274.47007
[15] Schechter M., Whitley R.: Best Fredholm perturbation theorems. Studia Math. 90 (1988), 175-190. MR 0959522 | Zbl 0611.47010
[16] Sedaev A.A.: The structure of certain linear operators (in Russian). Mat. Issled. 5 (1970), 166-175. MR 43#2540; Zbl 247#47005. MR 0276800
[17] Tylli H.-O.: On the asymptotic behaviour of some quantities related to semi-Fredholm operators. J. London Math. Soc. (2) 31 (1985), 340-348. MR 0809955 | Zbl 0582.47004
[18] Weis L.: Über striktle singulare und striktle cosingulare Operatoren in Banachräumen. Diss., Univ. Bonn, 1974.
[19] Zemánek J.: Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour. Studia Math. 80 (1984), 219-234. MR 0783991
Search
Partner of
