|
|
| |
| Approximate Representation of Bergman Submodules |
| |
Citation： |
Chong ZHAO.Approximate Representation of Bergman Submodules[J].Chinese Annals of Mathematics B,2016,37(2):221~234 |
| Page view： 6796
Net amount： 4099 |
Authors： |
Chong ZHAO; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11271075, 11371096), Shandong Province
Natural Science Foundation (No.ZR2014AQ009) and the Fundamental
Research Funds of Shandong University (No.2015GN017). |
|
|
| Abstract： |
In the present paper, the author shows that if a homogeneous
submodule $\mathcal{M}$ of the Bergman module $L_a^2(B_d)$ satisfies
$$
P_{\mathcal{M}}-\sum_iM_{z^i}P_{\mathcal{M}}M_{z^i}^*\leq\frac{c}{N+1}P_{\mathcal{M}}
$$
for some number $c>0$, then there is a sequence $\{f_j\}$ of
multipliers and a positive number $c'$ such that
$c'P_{\mathcal{M}}\leq\sum\limits_jM_{f_j}M_{f_j}^*\leq
P_{\mathcal{M}}$, i.e., $\mathcal{M}$ is approximately
representable. The author also proves that approximately
representable homogeneous submodules are $p$-essentially normal for
$p>d$. |
Keywords： |
Approximate representation, Essential normality, Bergman submodule |
Classification： |
47A13, 46E22 |
|
|
Download PDF Full-Text
|
|
|
|
