The Root Operator on Invariant Subspaces of the Weighted Bergman Space
Received:July 06, 2009  Revised:December 04, 2009
Key Word: root operator   index   weighted Bergman space   invariant subspace.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.10671028; 10971020).
Author NameAffiliation
Xiao Yang ZHOU School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China 
Xiu Ying SHI School of Continuing Education, Chifeng University, Inner Mongolia 024000, P. R. China 
Yu Feng LU School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China 
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Abstract:
      In this paper, for an invariant subspace $I$ of the weighted Bergman space, the weighted root operator is defined. We study the weighted root operator and obtain its fundamental properties when the invariant subspace $I$ has finite index. Furthermore, we give some examples of the root operator and estimate ranks of the operators.
Citation:
DOI:10.3770/j.issn:1000-341X.2010.01.005
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