## Separating vectors for operators

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## Abstract:

It is an open problem whether every one-dimensional extension of a triangular operator admits a separating vector. We prove that the answer is positive for many triangular Hilbert space operators, and in particular, for strictly triangular operators. This is revealing, because two-dimensional extensions of such operators can fail to have separating vectors.## References

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## Additional Information

**D. Han**- Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- Email: dhan@pegasus.cc.ucf.edu
**D. Larson**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 110365
- Email: larson@math.tamu.edu
**Z. Pan**- Affiliation: Department of Mathematics, Saginaw Valley State University, University Center, Michigan 48710
- Email: Pan@svsu.edu
**W. Wogen**- Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
- MR Author ID: 183945
- Email: wrw@math.unc.edu
- Received by editor(s): November 3, 2004
- Received by editor(s) in revised form: September 7, 2005
- Published electronically: October 19, 2006
- Additional Notes: The second author was supported in part by NSF grant DMS-0070796
- Communicated by: Joseph A. Ball
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**135**(2007), 713-723 - MSC (2000): Primary 47A10, 47A65, 47A66, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-06-08486-3
- MathSciNet review: 2262867