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Finite-dimensional left ideals in the duals of introverted spaces


Authors: M. Filali and M. Sangani Monfared
Journal: Proc. Amer. Math. Soc. 139 (2011), 3645-3656
MSC (2010): Primary 46H10, 46H15, 46H25, 43A20, 43A60
DOI: https://doi.org/10.1090/S0002-9939-2011-10784-6
Published electronically: February 24, 2011
MathSciNet review: 2813394
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Abstract: We use representations of a Banach algebra $ A$ to completely characterize all finite-dimensional left ideals in the dual of introverted subspaces of $ A^*$ and in particular in the double dual $ A^{**}$. We give sufficient conditions under which such ideals always exist and are direct sums of one-dimensional left ideals.


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Additional Information

M. Filali
Affiliation: Department of Mathematical Sciences, University of Oulu, Oulu 90014, Finland
Email: mahmoud.filali@oulu.fi

M. Sangani Monfared
Affiliation: Department of Mathematics and Statistics, University of Windsor, Windsor, ON, N9B 3P4, Canada
Email: monfared@uwindsor.ca

DOI: https://doi.org/10.1090/S0002-9939-2011-10784-6
Received by editor(s): March 31, 2010
Received by editor(s) in revised form: September 2, 2010
Published electronically: February 24, 2011
Additional Notes: The second author was partially supported by NSERC
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2011 American Mathematical Society