On the closure of the complex symmetric operators: compact operators and weighted shifts

Details On the closure of the complex symmetric operators: compact operators and weighted shifts On the closure of the complex symmetric operators: compact operators and weighted shifts

2011-06-23

arxiv.org/abs/1106.4855v1

Mathematics

Functional Analysis

19 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the closure of the complex symmetric operators: compact operators and weighted shifts does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the closure of the complex symmetric operators: compact operators and weighted shifts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the closure of the complex symmetric operators: compact operators and weighted shifts will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-393480