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On the Closure of the Complex Symmetric Operators: Compact Operators and Weighted Shifts by Garcia, Stephan Ramon; Poore, Daniel E. is a scholarly article available to read on EtoBox.

What is On the Closure of the Complex Symmetric Operators: Compact Operators and Weighted Shifts about?

We study the closure $\bar{CSO}$ 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 $\bar{CSO}$ is complex symmetric. Using a construction of Kakutani as motivation, we also describe many properties of weighted shifts in $\bar{CSO} \backslash CSO$. In particular, we show that weighted shifts which demonstrate a type of approximate self-similarity belong to $\bar{CSO}\backslash CSO$. As a byproduct of our treatment of weighted shifts, we explain several ways in which our result on compact operators is optimal.

Author

Garcia, Stephan Ramon; Poore, Daniel E.

Published

2011

Language

EN