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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
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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.
References:
-
- [AS1]
- E. Azoff and H. Shehada, Algebras generated by mutually orthogonal idempotent operators, J. Operator Theory, 29 (1993), 249-267. MR 1284883 (95h:47063)
- [AS2]
- E. Azoff and H. Shehada, Literal embeddings of linear spaces of operators, Indiana Univ. Math. J., 42 (1993), 571-589. MR 1237060 (94i:47068)
- [Co]
- J. Conway, A Course in Functional Analysis, Springer-Verlag, New York Inc., 1985. MR 0768926 (86h:46001)
- [GLW]
- W. Gong, D. Larson and W. Wogen, Two results on separating vectors, Indiana University Math. J., 43(1994), 1159-1165. MR 1322615 (96h:47050)
- [HN]
- D. Hadwin and E. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory, 7(1982), 3-23. MR 0650190 (83f:47033)
- [HLPW]
- D. Han, D. Larson, Z. Pan and W. Wogen, Extensions of operators, Indiana University Math. J., 53 (2004), no. 4, 1151-1169. MR 2095452
- [H]
- D. Herrero, Triangular Operators, Bull. London Math. Soc. 23(1991), 513-554. MR 1135184 (92k:47001)
- [HLW]
- D. Herrero, D. Larson and W. Wogen, Semitriangular operators, Houston J. Math., 17(1991), 477-499. MR 1147270 (92m:47037)
- [L]
- D. R. Larson, Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math., 110(1988), 283-299. MR 0935008 (89d:47096)
- [LW1]
- D. Larson and W. Wogen, Reflexivity properties of
 , J. Funct. Anal., 92(1990), 448-467. MR 1069253 (91i:47010) - [LW2]
- D. Larson and W. Wogen, Some problems on triangular and semitriangular operators, Contemporary Mathematics, 120(1991), 97-100. MR 1126279 (92i:47019)
- [LW3]
- D. Larson and W. Wogen, Extensions of normal operators, Integr. Equat. Oper. Th., 20(1994), 325-334. MR 1299891 (96b:47024)
- [LW4]
- D. Larson and W. Wogen, Extensions of bitriangular operators, Integr. Equat. Oper. Th., 25(1996), 216-223. MR 1388681 (97d:47027)
- [S]
- A. Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory, Math. Surveys, Amer. Math. Soc., Providence R. I. (1974), no. 13. MR 0361899 (50:14341)
- [W]
- W. Wogen, Some counterexamples in nonselfadjoint algebras, Ann. Math., 126 (1987), 415-427. MR 0908152 (89b:47066)
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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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