Operational quantities
Martinón, Antonio
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 471-484 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1997-01-01
Classification:  47A53,  47A55 
@article{118946,
     author = {Antonio Martin\'on},
     title = {Operational quantities},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {471-484},
     zbl = {1119.47014},
     mrnumber = {1485069},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118946}
}

Martinón, Antonio. Operational quantities. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 471-484. http://gdmltest.u-ga.fr/item/118946/

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. (1985)

Galaz-Fontes F. Measures of noncompactness and upper semi-Fredholm perturbation theorems, Proc. Amer. Math. Soc. 118 (1993), 891-897. (1993) | MR 1151810 | Zbl 0782.47013

Goldberg S. Unbounded Linear Operators, McGraw-Hill, New York, 1966. | MR 0200692 | Zbl 1152.47001

González M.; Martinón A. Operational quantities derived from the norm and measures of noncompactness, Proc. R. Ir. Acad. 91 A (1991), 63-70. (1991) | MR 1173159

González M.; Martinón A. Operational quantities derived from the norm and generalized Fredholm theory, Comment. Math. Univ. Carolinae 32 (1991), 645-657. (1991) | MR 1159811

González M.; Martinón A. Fredholm theory and space ideals, Boll. U.M.I. 7 B (1993), 473-488. (1993) | MR 1223653

González M.; Martinón A. Note on operational quantities and the Mil'man isometry spectrum, Rev. Acad. Canar. Cienc. 3 (1991), 103-111. (1991) | MR 1175602

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

González M.; Martinón A. Operational quantities characterizing the semi-Fredholm operators, Studia Math. 114 (1995), 13-27. (1995) | MR 1330214

Lebow A.; Schechter M. Semigroups of operators and measures of noncompactness, J. Funct. Anal. 7 (1971), 1-26. (1971) | MR 0273422 | Zbl 0209.45002

Martinón A. Generating real maps on a biordered set, Comment. Math. Univ. Carolinae 32 (1991), 265-272. (1991) | MR 1137787

Pietsch A. Operators Ideals, North-Holland, Amsterdam, 1980. | MR 0582655

Rakocevic V. Measures of non-strict-singularity of operators, Mat. Vesnik 35 (1983), 79-82. (1983) | MR 0724182 | Zbl 0532.47006

Schechter M. Quantities related to strictly singular operators, Indiana Univ. Math. J. 21 (1972), 1061-1071. (1972) | MR 0295103 | Zbl 0274.47007

Schechter M.; Whitley R. Best Fredholm perturbation theorems, Studia Math. 90 (1988), 175-190. (1988) | MR 0959522 | Zbl 0611.47010

Sedaev A.A. The structure of certain linear operators (in Russian), Mat. Issled. 5 (1970), 166-175. MR 43#2540; Zbl 247#47005. (1970) | MR 0276800

Tylli H.-O. On the asymptotic behaviour of some quantities related to semi-Fredholm operators, J. London Math. Soc. (2) 31 (1985), 340-348. (1985) | MR 0809955 | Zbl 0582.47004

Weis L. Über striktle singulare und striktle cosingulare Operatoren in Banachräumen, Diss., Univ. Bonn, 1974.

Zemánek J. Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), 219-234. (1984) | MR 0783991