Structure of Quasi-Invariant Vector Spaces
Received:July 04, 1997  
Key Words: vector space   quasi-invariant.  
Fund Project:Supported by the National Natural Science Foundation of China(19771014) and Liaoning Province(972208)
Author NameAffiliation
FENG Hong Dept. of Appl. Math.
Dalian University of Technology
116024 
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Abstract:
      Let V be a vector space over a field F and G a group of linear transformations in V. It is proved in this note that for any subspace U?V, if dim U/(U∩g(U))≤ 1, for any g∈G, then there is a g∈ G such that U∩g(U) is a G-invariant subspace, or there is an x∈V\U such that U+ is a G-invariant subspace. So a vector-space analog of Brailovsky's results on quasi-invariant sets is given.
Citation:
DOI:10.3770/j.issn:1000-341X.2000.02.008
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