Measures of noncompactness and upper semi-Fredholm perturbation theorems

Galaz-Fontes, Fernando

doi:10.1090/S0002-9939-1993-1151810-3

Measures of noncompactness and upper semi-Fredholm perturbation theorems
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by Fernando Galaz-Fontes PDF

Proc. Amer. Math. Soc. 118 (1993), 891-897 Request permission

Abstract:

We introduce the concept of a perturbation function, which allows us to give a general approach to the question of obtaining perturbation theorems for upper semi-Fredholm operators. Also, we show that the usual measures of noncompactness of continuous linear operators, as well as other related quantities, are perturbation functions.

References

Kari Astala and Hans-Olav Tylli, On the bounded compact approximation property and measures of noncompactness, J. Funct. Anal. 70 (1987), no. 2, 388–401. MR 874062, DOI 10.1016/0022-1236(87)90118-2
D. E. Edmunds and W. D. Evans, Spectral theory and differential operators, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1987. Oxford Science Publications. MR 929030

Investigation of some properties of bounded linear operators in connection with their

norms

29

Seymour Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0200692

Über analytische störungen und den Index von Fredholm operatoren auf Banachraumen

Arnold Lebow and Martin Schechter, Semigroups of operators and measures of noncompactness, J. Functional Analysis 7 (1971), 1–26. MR 0273422, DOI 10.1016/0022-1236(71)90041-3
Roger D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 37 (1970), 473–478. MR 264434
Martin Schechter, Riesz operators and Fredholm perturbations, Bull. Amer. Math. Soc. 74 (1968), 1139–1144. MR 231222, DOI 10.1090/S0002-9904-1968-12083-X
Martin Schechter, Quantities related to strictly singular operators, Indiana Univ. Math. J. 21 (1971/72), 1061–1071. MR 295103, DOI 10.1512/iumj.1972.21.21085
M. Schechter and Robert Whitley, Best Fredholm perturbation theorems, Studia Math. 90 (1988), no. 3, 175–190. MR 959522, DOI 10.4064/sm-90-3-175-190
Hans-Olav Tylli, On the asymptotic behaviour of some quantities related to semi-Fredholm operators, J. London Math. Soc. (2) 31 (1985), no. 2, 340–348. MR 809955, DOI 10.1112/jlms/s2-31.2.340
Jaroslav Zemánek, Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), no. 3, 219–234. MR 783991, DOI 10.4064/sm-80-3-219-234