Integral Equations and Operator Theory

, Volume 67, Issue 2, pp 151–161

Quasi-wandering Subspaces in the Bergman Space

Article

DOI: 10.1007/s00020-010-1744-4

Cite this article as:
Izuchi, K.J., Izuchi, K.H. & Izuchi, Y. Integr. Equ. Oper. Theory (2010) 67: 151. doi:10.1007/s00020-010-1744-4
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Abstract

Let \({\mathcal{B}}\) be the Bergman shift on the Bergman space \({L_a^2}\) over the open unit disk and let I be a nontrivial invariant subspace of \({L_a^2}\). Let PI be the orthogonal projection from \({L_a^2}\) onto I. It is proved that \({P_I\mathcal{B}(L_a^2 \ominus I)}\) is not dense in I if and only if \({I \cap \mathcal{D} \ne \{0\}}\), where \({\mathcal{D}}\) is the Dirichlet space. It is also discussed some related topics.

Mathematics Subject Classification (2010)

Primary 47A15Secondary 32A3547B35

Keywords

Bergman spaceinvariant subspacequasi-wandering subspace

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Department of MathematicsNiigata UniversityNiigataJapan
  2. 2.Institute of Basic ScienceKorea UniversitySeoulRepublic of Korea
  3. 3.NiigataJapan