Cuellar, Jorge; Dynin, Alexander; Dynin, Svetlana Fredholm operator families. I. (English) Zbl 0522.47010 Integral Equations Oper. Theory 6, 853-862 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 1 Document MSC: 47A53 (Semi-) Fredholm operators; index theories 47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) Keywords:semi-Fredholm operator families; stability properties; collectively compact sequence × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Adasch, N., Keim, B., Ernst, D.: Topological Vector Spaces. The Theory without Convexity Conditions. Springer-Verlag. LNM 639. Berlin, Heidelberg, New York (1978). · Zbl 0397.46005 [2] Anselone, P.M.: Collectively Compact Operator Approximation and Applications to Integral Equations. Prentice-Hall, Englewood Cliffs, New Jersey (1971). · Zbl 0228.47001 [3] Berger, R.: Fredholmoperatoren in separierten topologischen Vektorräumen und lokalbeschränkten Räumen. Diplomarbeit. Johannes Gutenberg-Universität. Mainz (1969). [4] Cuellar, J.: Fredholmoperatoren auf lokalbeschränkten Räumen mit Anwendungen auf elliptische Gleichungen. Dissertation. Johannes Gutenberg-Universität. Mainz (1982). · Zbl 0552.47008 [5] Deprit, A.: Quelques classes d’endomorphismes d’espaces localment convex séparés. Bull. el. sci. Acad. Roy. Belg., 43, 252–272 (1975). [6] De Pree, J.D., Higgins, J.A.: Collectively Compact Sets of Linear Operators. Math. Z. 115, 366–370 (1970). · doi:10.1007/BF01131309 [7] Dolganova, S.: Semi-Fredholm Operator Families on Topological Vector Spaces. (Russian). Uspekhi Mat. Nauk, 27:4, 211–212 (1972). [8] Goldberg, S.: Perturbations of Semi-Fredholm Operators by Operators Converging to Zero Compactly. Proc. Amer. Math. Soc. 45, 93–98 (1974). · Zbl 0258.47015 · doi:10.1090/S0002-9939-1974-0346579-4 [9] Gramsch, B.: Ein Schema zur Theorie Fredholmscher Endomorphismen und eine Anwendung auf die Idealkette der Hilberträume. Math. Annalen 171, 263–272 (1967). · Zbl 0173.42703 · doi:10.1007/BF01350734 [10] Gramsch, B., Kaballo, W.: Spectral Theory for Fredholm Operators. In: Functional Analysis: Surveys and Recent Results II, 319–342. Ed.: K.D. Bierstedt, B. Fuchssteiner. North-Holland. Amsterdam (1980). · Zbl 0442.47008 [11] Hörmander, L.: On the Index of Pseudodiffential Operators. In: Elliptische Differentialgleichungen. Band II. 127–146. Akademie-Verlag. Berlin (1971). [12] Kaballo, W.: Holomorphe Semifredholm-Operatorfunktionen in lokalkonvexen Räumen. Diplomarbeit. Kaiserslautern (1973). [13] Kaballo, W.: Holomorphe Semifredholmfunktionen mit Anwendungen auf Differential- und Pseudodifferentialoperatoren. Dissertation. Kaiserslautern (1974). [14] Pietsch, A.: Zur Theorie der {\(\sigma\)}-Transformationen in lokalkonvexen Vektorräumen. Math. Nachr. 21, 347–369 (1960). · Zbl 0095.30903 · doi:10.1002/mana.19600210604 [15] Segal, G.: Fredholm Complexes. Quart. J. Math. Oxford (2), 21, 385–402 (1970). · Zbl 0213.25403 · doi:10.1093/qmath/21.4.385 [16] Sobolev, S.L.: Some remarks about the numerical solution of integral equations. Izvestia Acad. Sci. USSR, vol 20, n{\(\deg\)} 4, 413–436 (1956). [17] Vainikko, G.M.: Regular Convergence of Operators and Approximate Solution of Equations. Jour. of Sov. Math. 15 (6), 675–705 (1981). Translated from Itogi Nauki i Tekhniki, Seriya Mat. Analiz, 16, 5–53 (1979). · Zbl 0582.65046 · doi:10.1007/BF01377042 [18] Williamson. J.H.: Compact Linear Operators in Linear Topological Spaces. Jour. Lond. Math. Soc. 29, 149–156 (1954). · Zbl 0055.10901 · doi:10.1112/jlms/s1-29.2.149 [19] Zaidenberg, M.G., Krein S.G., Kuchment, P.A., Pankov, A.A.: Banach Bundles and Linear Operators. Russian Math. Surveys 30:5, 115–175 (1975). Translated from Uspekhi mat. Nauk 30:5, 101–157 (1975). · Zbl 0335.47017 · doi:10.1070/RM1975v030n05ABEH001523 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.