Finite-codimensional invariant subspaces of Bergman spaces
HTML articles powered by AMS MathViewer
- by Sheldon Axler and Paul Bourdon PDF
- Trans. Amer. Math. Soc. 306 (1988), 805-817 Request permission
Abstract:
For a large class of bounded domains in $\mathbb {C}$, we describe those finite codimensional subspaces of the Bergman space that are invariant under multiplication by $z$. Using different techniques for certain domains in ${\mathbb {C}^N}$, we describe those finite codimensional subspaces of the Bergman space that are invariant under multiplication by all the coordinate functions.References
- O. P. Agrawal, D. N. Clark, and R. G. Douglas, Invariant subspaces in the polydisk, Pacific J. Math. 121 (1986), no. 1, 1–11. MR 815027, DOI 10.2140/pjm.1986.121.1
- P. R. Ahern and D. N. Clark, Invariant subspaces and analytic continuation in several variables. , J. Math. Mech. 19 (1969/1970), 963–969. MR 0261340
- 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
- Hari Bercovici, A question on invariant subspaces of Bergman spaces, Proc. Amer. Math. Soc. 103 (1988), no. 3, 759–760. MR 947653, DOI 10.1090/S0002-9939-1988-0947653-1
- Hari Bercovici, The algebra of multiplication operators on Bergman spaces, Arch. Math. (Basel) 48 (1987), no. 2, 165–174. MR 878428, DOI 10.1007/BF01189287 Nicolas Bourbaki, General topology, Part 1, Addison-Wesley, Reading, Mass., 1966.
- 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 Per Lindberg, ${L^p}$-approximation by analytic functions in an open region, Uppsala University (Sweden) Department of Mathematics Report No. 7, 1977.
- Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 49–128. MR 0361899
- Lawrence Zalcman, Bounded analytic functions on domains of infinite connectivity, Trans. Amer. Math. Soc. 144 (1969), 241–269. MR 252665, DOI 10.1090/S0002-9947-1969-0252665-2
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 306 (1988), 805-817
- MSC: Primary 46E15; Secondary 32A10, 32H20, 46J15, 47B38
- DOI: https://doi.org/10.1090/S0002-9947-1988-0933319-5
- MathSciNet review: 933319