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Separating vectors for operators |
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| Authors: | D. Han D. Larson Z. Pan W. Wogen |
| Affiliation: | Department of Mathematics, University of Central Florida, Orlando, Florida 32816 ; Department of Mathematics, Texas A&M University, College Station, Texas 77843 ; Department of Mathematics, Saginaw Valley State University, University Center, Michigan 48710 ; Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599 |
| 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. |
| Keywords: | Separating vector extension of operators triangular operator integral domain |
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