Invariant subspaces with finite codimension in Bergman spaces

Aleman, Alexandru

doi:10.1090/S0002-9947-1992-1028755-6

Invariant subspaces with finite codimension in Bergman spaces
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by Alexandru Aleman

Trans. Amer. Math. Soc. 330 (1992), 531-544

DOI: https://doi.org/10.1090/S0002-9947-1992-1028755-6

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Abstract:

For an arbitrary bounded domain in $\mathbb {C}$ there are described those finite codimensional subspaces of the Bergman space that are invariant under multiplication by $z$.

References

Sheldon Axler, Multiplication operators on Bergman spaces, J. Reine Angew. Math. 336 (1982), 26–44. MR 671320, DOI 10.1515/crll.1982.336.26
Sheldon Axler, John B. Conway, and Gerard McDonald, Toeplitz operators on Bergman spaces, Canadian J. Math. 34 (1982), no. 2, 466–483. MR 658979, DOI 10.4153/CJM-1982-031-1
Sheldon Axler and Paul Bourdon, Finite-codimensional invariant subspaces of Bergman spaces, Trans. Amer. Math. Soc. 306 (1988), no. 2, 805–817. MR 933319, DOI 10.1090/S0002-9947-1988-0933319-5
Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
T. W. Gamelin and John Garnett, Distinguished homomorphisms and fiber algebras, Amer. J. Math. 92 (1970), 455–474. MR 303296, DOI 10.2307/2373334
Ralph Gellar, Operators commuting with a weighted shift, Proc. Amer. Math. Soc. 23 (1969), 538–545. MR 259641, DOI 10.1090/S0002-9939-1969-0259641-X