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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Separating vectors for operators
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by D. Han, D. Larson, Z. Pan and W. Wogen PDF
Proc. Amer. Math. Soc. 135 (2007), 713-723 Request permission

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
  • 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