Abstract:We prove that the set of all complex symmetric operators on a separable, infinite-dimensional Hilbert space is not norm closed.
- Stephan Ramon Garcia and Mihai Putinar, Complex symmetric operators and applications. II, Trans. Amer. Math. Soc. 359 (2007), no. 8, 3913–3931. MR 2302518, DOI 10.1090/S0002-9947-07-04213-4
- Stephan Ramon Garcia and Warren R. Wogen, Complex symmetric partial isometries, J. Funct. Anal. 257 (2009), no. 4, 1251–1260. MR 2535469, DOI 10.1016/j.jfa.2009.04.005
- Sen Zhu, Chun Guang Li, and You Qing Ji, The class of complex symmetric operators is not norm closed, Proc. Amer. Math. Soc. 140 (2012), no. 5, 1705–1708. MR 2869154, DOI 10.1090/S0002-9939-2011-11345-5
- Stephan Ramon Garcia
- Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
- MR Author ID: 726101
- Email: Stephan.Garcia@pomona.edu
- Received by editor(s): March 27, 2011
- Received by editor(s) in revised form: June 30, 2011
- Published electronically: June 14, 2012
- Additional Notes: This work partially supported by National Science Foundation Grant DMS-1001614.
- Communicated by: Marius Junge
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 141 (2013), 549-549
- MSC (2010): Primary 47A05, 47B35, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-2012-11347-4
- MathSciNet review: 2996959