Geodesic
Certain Invariant Subspaces of H 2 and L 2 on a Bidisc
Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1272-1280

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

We let T 2 be the torus that is the cartesian product of 2 unit circles in C. The usual Lebesgue spaces, with respect to the Haar measure m of T 2, are denoted by Lp = Lp (T 2), and Hp = Hp (T 2) is the space of all f in LP whose Fourier coefficients are 0 as soon as at least one component of (j, l) is negative.A closed subspace M of L 2 is said to be invariant if Whenever this is the case, it follows that fM ⊂ M for every f in H ∞. One can ask for a classification or an explicit description (in some sense) of all invariant subspaces of L 2, but this seems out of reach. 
Nakazi, Takahiko. Certain Invariant Subspaces of H 2 and L 2 on a Bidisc. Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1272-1280. doi: 10.4153/CJM-1988-055-6
@article{10_4153_CJM_1988_055_6,
     author = {Nakazi, Takahiko},
     title = {Certain {Invariant} {Subspaces} of {H} 2 and {L} 2 on a {Bidisc}},
     journal = {Canadian journal of mathematics},
     pages = {1272--1280},
     year = {1988},
     volume = {40},
     number = {5},
     doi = {10.4153/CJM-1988-055-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-055-6/}
}
TY  - JOUR
AU  - Nakazi, Takahiko
TI  - Certain Invariant Subspaces of H 2 and L 2 on a Bidisc
JO  - Canadian journal of mathematics
PY  - 1988
SP  - 1272
EP  - 1280
VL  - 40
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-055-6/
DO  - 10.4153/CJM-1988-055-6
ID  - 10_4153_CJM_1988_055_6
ER  - 
%0 Journal Article
%A Nakazi, Takahiko
%T Certain Invariant Subspaces of H 2 and L 2 on a Bidisc
%J Canadian journal of mathematics
%D 1988
%P 1272-1280
%V 40
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1988-055-6/
%R 10.4153/CJM-1988-055-6
%F 10_4153_CJM_1988_055_6

[1] 1. Curto, R. E., Muhly, P. S., Nakazi, T. and Yamamoto, T., On superalgebras of the poly disc algebra, Acta Sci. Math. 51 (1987), 413–421. Google Scholar

[2] 2. Helson, H., Lectures on invariant subspaces (Academic Press, New York and London, 1964). Google Scholar

[3] 3. Helson, H. and Lowdenslager, D., Invariant subspaces, Proc. Int. Symp. Linear Spaces, Jerusalem, 1960 (MacMillan (Pergamon), 1961), 251–262. Google Scholar

[4] 4. Nakazi, T., Invariant subspaces of unitary operators, J. Math. Soc. Japan 34 (1982), 627–635. Google Scholar

[5] 5. Nakazi, T., Invariant subspaces of weak* Dirichlet algebras, Pacific J. Math. 69 (1977), 151–167. Google Scholar

[6] 6. Rudin, W., Function theory in polydiscs (Benjamin, New York, 1969). Google Scholar

Cité par Sources :