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On the norm closure problem for complex symmetric operators


Authors: Stephan Ramon Garcia and Daniel E. Poore
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
Published electronically: June 14, 2012
MathSciNet review: 2996959
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the set of all complex symmetric operators on a separable, infinite-dimensional Hilbert space is not norm closed.


References [Enhancements On Off] (What's this?)

  • 1. Stephan Ramon Garcia and Mihai Putinar.
    Complex symmetric operators and applications. II.
    Trans. Amer. Math. Soc., 359(8):3913-3931 (electronic), 2007. MR 2302518 (2008b:47005)
  • 2. Stephan Ramon Garcia and Warren R. Wogen.
    Complex symmetric partial isometries.
    J. Funct. Anal., 257(4):1251-1260, 2009. MR 2535469 (2011g:47005)
  • 3. Sen Zhu, Chun Guang Li, and You Qing Ji.
    The class of complex symmetric operators is not norm closed.
    Proc. Amer. Math. Soc., 140(5):1705-1708, 2012. MR 2869154

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Additional Information

Stephan Ramon Garcia
Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
Email: Stephan.Garcia@pomona.edu

Daniel E. Poore
Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711

DOI: https://doi.org/10.1090/S0002-9939-2012-11347-4
Keywords: Complex symmetric operator, norm closure, Hilbert space
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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