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THE CLASS OF COMPLEX SYMMETRIC OPERATORS IS NOT NORM CLOSED.
- Source :
-
Proceedings of the American Mathematical Society . May2012, Vol. 140 Issue 5, p1705-1708. 4p. - Publication Year :
- 2012
-
Abstract
- An operator T ∊ B(H) is complex symmetric if there exists a conjugate-linear, isometric involution C : H →H so that CTC = T. In this paper, a class of complex symmetric operators on finite dimensional Hilbert spaces is constructed. As an application, it is shown that Kakutani's unilateral weighted shift operator is not complex symmetric; however, it is a norm limit of complex symmetric operators. This gives a negative answer to a question of S. Garcia and W. Wogen: that is, whether or not the class of complex symmetric operators is norm closed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 140
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 70547605
- Full Text :
- https://doi.org/10.1090/S0002-9939-2011-11345-5