Geodesic
On~invariant subspaces of multiple weighted shift operators
Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 345-365

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Unilateral and bilateral multiple weighted shift operators whose weight sequences consist of invertible operators are studied. Under a certain condition on the decrease of the weight sequence the invariant subspaces of unilateral shift operators with finite multiplicity are found, and a reducibility condition for bilateral weighted shift operators (of any multiplicity) is obtained. In some cases the reducing subspaces of these operators are described. Bibliography: 11 titles. 
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     author = {V. S. Pilidi},
     title = {On~invariant subspaces of multiple weighted shift operators},
     journal = {Izvestiya. Mathematics },
     pages = {345--365},
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     volume = {14},
     number = {2},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a7/}
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V. S. Pilidi. On~invariant subspaces of multiple weighted shift operators. Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 345-365. http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a7/