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Separating vectors for operators


Authors: D. Han, D. Larson, Z. Pan and W. Wogen
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
Published electronically: October 19, 2006
MathSciNet review: 2262867
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Abstract | References | Similar Articles | Additional Information

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.


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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
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
Email: wrw@math.unc.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08486-3
Keywords: Separating vector, extension of operators, triangular operator, integral domain
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
Article copyright: © Copyright 2006 American Mathematical Society

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