Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590884 | Journal of Functional Analysis | 2013 | 22 Pages |
Abstract
We study the closure of the set CSO of all complex symmetric operators on a separable, infinite-dimensional, complex Hilbert space. Among other things, we prove that every compact operator in is complex symmetric. Using a construction of Kakutani as motivation, we also describe many properties of weighted shifts in . In particular, we show that weighted shifts which demonstrate a type of approximate self-similarity belong to . As a byproduct of our treatment of weighted shifts, we explain several ways in which our result on compact operators is optimal.
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Physical Sciences and Engineering
Mathematics
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