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