Joint Reducing Subspaces of Multiplication Operators and Weight of Multi-variable Bergman Spaces
| Autor: | Hansong Huang, Peng Ling |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Class (set theory) Applied Mathematics General Mathematics 010102 general mathematics 01 natural sciences Linear subspace 010104 statistics & probability symbols.namesake Von Neumann algebra Bergman space symbols Multiplication 0101 mathematics Tuple Joint (audio engineering) Von Neumann architecture Mathematics |
| Zdroj: | Chinese Annals of Mathematics, Series B. 40:187-198 |
| ISSN: | 1860-6261 0252-9599 |
| Popis: | This paper mainly concerns a tuple of multiplication operators defined on the weighted and unweighted multi-variable Bergman spaces, their joint reducing subspaces and the von Neumann algebra generated by the orthogonal projections onto these subspaces. It is found that the weights play an important role in the structures of lattices of joint reducing subspaces and of associated von Neumann algebras. Also, a class of special weights is taken into account. Under a mild condition it is proved that if those multiplication operators are defined by the same symbols, then the corresponding von Neumann algebras are *-isomorphic to the one defined on the unweighted Bergman space. |
| Databáze: | OpenAIRE |
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