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5. ,(®) < oo, ®' eine strikt singuliire Storung von®. ,(®'l < oo. ,(®). Es sei zuerst gezeigt, daB auch /I~J<>->, strikt singular ist: Angenommen, dies sei nicht der Fall. Dann gibt es einen unendlichdimensionalen abgeschlossenen Teilraum ~ von ®', auf dem II~ einen Homoomorphismus definiert. Es folgt, daB II~~ unendlichdimensional und abgeschlossen ist. Da ®/® endlichdimensional ist, kann II<>->= Il<>->t®Il~ auf ~ nur einen endlichdimensionalen Nullraum m' haben, ~ = ~' Ei3 m'. II<>-> ist auf ~' eineindeutig.

Math. Soc. Transl. Ser. 2 13, 185--264 (1960). Vbersetzt aus: Usp. Mat. Nauk 12, 2 (74), 43-118 (1957). Index abgeschlossener Operatoren 119 [6] IIALMos, P. , and G. LUMER: Square roots of operators II. Proc. Am. Math. Soc. 1), 589-595 (1954). : Vektorraumbtindel und der Raum der Fredholmoperatoren. Math. Ann. 160, 129-142 (1965). [8] JAMES, R. : Bases and reflexivity of Banach spaces. Ann. Math. 52, 518-527 (1950). : Perturbation theory for nullity, deficiency and other quantities of linear operators.

Beweis: Es ist V = I+ T. Die Einschrankung von I auf ® ist ein (®, (S't x '{)))-SF-Operator mit

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