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- Title
Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball.
- Authors
Shi, Yan Yue; Zhang, Bo; Tang, Xu; Lu, Yu Feng
- Abstract
In this paper, we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B 2 . It is proved that each minimal reducing subspace M is finite dimensional, and if dim M ≥ 3, then M is induced by a monomial. Furthermore, the structure of commutant algebra ν (T w ¯ N z N ) := { M w N ∗ M z N , M z N ∗ M w N } ′ is determined by N and the two dimensional minimal reducing subspaces of T w ¯ N z N . We also give some interesting examples.
- Subjects
VON Neumann, John, 1903-1957; TOEPLITZ operators; UNIT ball (Mathematics); BERGMAN spaces; VON Neumann algebras
- Publication
Acta Mathematica Sinica, 2024, Vol 40, Issue 7, p1767
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-024-2709-x