Geodesic
Invariant Complements to Closed Invariant Subspaces
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 139-147

Voir la notice de l'article provenant de la source Cambridge University Press

The question under what conditions a closed invariant subspace possesses a closed invariant complement is of major importance in operator theory. In general it remains unanswered. In this paper we drop the requirement that the invariant complement be closed. We show in section 1 that the question is answerable under fairly mild conditions for a quasinilpotent operator (Theorem 1.5). These conditions will cover the case of a quasinilpotent operator with dense range and no point spectrum. In section 2 we discuss the consequences for the Volterra operator V. Since V is unicellular, its proper closed invariant subspaces do not possess closed invariant complements. However, they are all algebraically complemented (Proposition 2.1). 
Thomas, M. P. Invariant Complements to Closed Invariant Subspaces. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 139-147. doi: 10.4153/CJM-1979-015-1
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