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Separating vectors for operators
Author(s):
D.
Han;
D.
Larson;
Z.
Pan;
W.
Wogen
Journal:
Proc. Amer. Math. Soc.
135
(2007),
713-723.
MSC (2000):
Primary 47A10, 47A65, 47A66, 47B99
Posted:
October 19, 2006
MathSciNet review:
2262867
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References |
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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:
10.1090/S0002-9939-06-08486-3
PII:
S 0002-9939(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
Posted:
October 19, 2006
Additional Notes:
The second author was supported in part by NSF grant DMS-0070796
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2006,
American Mathematical Society
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