Geodesic
Algebras Intertwining Normal and Decomposable Operators
Canadian journal of mathematics, Tome 31 (1979) no. 6, pp. 1339-1344

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

The celebrated result of Lomonosov [6] on the existence of invariant subspaces for operators commuting with a compact operator have been generalized in different directions (for example see [2], [7], [8], [9]). The main result of [9] (see also [7]) is: If is a norm closed algebra of (bounded) operators on an infinite dimensional (complex) Banach space , if K is a nonzero compact operator on , and if then has a non-trivial (closed) invariant subspace. In [7], it is mentioned that the above result holds if instead of compactness for K we assume that K is a non-invertible injective operator with a non-zero eigenvalue belonging to the class of decomposable, hyponormal, or subspectral operators. 
Jafarian, Ali A. Algebras Intertwining Normal and Decomposable Operators. Canadian journal of mathematics, Tome 31 (1979) no. 6, pp. 1339-1344. doi: 10.4153/CJM-1979-111-0
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