Finite rank operators in closed maximal triangular algebras II |
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| Authors: | Zhe Dong Shijie Lu |
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| Affiliation: | Institute of Mathematics, Fudan University, Shanghai 200433, People's Republic of China ; Department of Mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China |
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| Abstract: | In this paper, we discuss finite rank operators in a closed maximal triangular algebra  . Based on the following result that each finite rank operator of  can be written as a finite sum of rank one operators each belonging to  , we proved that  , where  , if  ; and  , if  . We also proved that the Erdos Density Theorem holds in  if and only if  is strongly reducible. |
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| Keywords: | Closed maximal triangular algebra finite rank operator $w^{*}$-closure |
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