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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1980_14_2_a7,
     author = {V. S. Pilidi},
     title = {On~invariant subspaces of multiple weighted shift operators},
     journal = {Izvestiya. Mathematics },
     pages = {345--365},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a7/}
}
TY  - JOUR
AU  - V. S. Pilidi
TI  - On~invariant subspaces of multiple weighted shift operators
JO  - Izvestiya. Mathematics 
PY  - 1980
SP  - 345
EP  - 365
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a7/
LA  - en
ID  - IM2_1980_14_2_a7
ER  - 
%0 Journal Article
%A V. S. Pilidi
%T On~invariant subspaces of multiple weighted shift operators
%J Izvestiya. Mathematics 
%D 1980
%P 345-365
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a7/
%G en
%F IM2_1980_14_2_a7
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/

[1] Donoghue W. F., “The lattice of invariant subspaces of a completely continuous quasinilpotent transformation”, Pacif. J. Math., 7:2 (1957), 1031–1035 | MR | Zbl

[2] Nikolskii N. K., “Ob invariantnykh podprostranstvakh vzveshennykh operatorov sdviga”, Matem. sb., 74:2 (1967), 172–190 | MR

[3] Lax P. D., “Translation invariant spaces”, Acta Math., 101:3, 4 (1959), 163–178 | DOI | MR | Zbl

[4] Halmos P. R., “Shifts on Hilbert spaces”, J. Reine und Angew. Math., 208:1,2 (1961), 102–112 | MR | Zbl

[5] Helson H., Lowdenslager D., “Invariant subspaces”, Proc. Intern. Symp. Linear Spaces (Jerusalem, 1960), Acad. Press, Pergamon Press, Jerusalem, Oxford, 1961, 251–262 | MR

[6] Lambert A., “Unitary equivalence and reducibility of invertibly weighted shifts”, Bull. Austral Math. Soc., 5:2 (1971), 157–173 | DOI | MR | Zbl

[7] Nordgren E. A., “Invariant subspaces of a direct sum of weighted shifts”, Proc. Amer. Math. Soc., 24:3 (1970), 424–428 | DOI | MR | Zbl

[8] Naimark M. A., Normirovannye koltsa, Nauka, M., 1968 | MR | Zbl

[9] Khalmosh P., Gilbertovo prostranstvo v zadachakh, Mir, M., 1970 | MR | Zbl

[10] Shabat B. V., Vvedenie v kompleksnyi analiz, ch. 1, Nauka, M., 1976 | MR

[11] Radijavi H., Rosenthal P., Invariant subspaces, Ergeb. Math., 77, Springer, Berlin, 1973