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Transactions of the American Mathematical Society

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On non-Archimedean Fréchet spaces with nuclear Köthe quotients


Author: Wiesław Sliwa
Journal: Trans. Amer. Math. Soc. 362 (2010), 3273-3288
MSC (2010): Primary 46S10, 46A04, 46A11, 46A35
DOI: https://doi.org/10.1090/S0002-9947-10-05033-6
Published electronically: January 21, 2010
MathSciNet review: 2592956
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Abstract: Assume that $ \mathbb{K}$ is a complete non-Archimedean valued field. We prove that every infinite-dimensional Fréchet-Montel space over $ \mathbb{K}$ which is not isomorphic to $ \mathbb{K}^{\mathbb{N}}$ has a nuclear Köthe quotient. If the field $ \mathbb{K}$ is non-spherically complete, we show that every infinite-dimensional Fréchet space of countable type over $ \mathbb{K}$ which is not isomorphic to the strong dual of a strict $ LB$-space has a nuclear Köthe quotient.


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Additional Information

Wiesław Sliwa
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland
Email: sliwa@amu.edu.pl

DOI: https://doi.org/10.1090/S0002-9947-10-05033-6
Keywords: Orthogonal basis, biorthogonal sequence, strict $LB$-space, nuclear K{\"o}the quotient.
Received by editor(s): November 12, 2007
Received by editor(s) in revised form: March 1, 2009
Published electronically: January 21, 2010
Additional Notes: The research of the author was supported in years 2007–2010 by Ministry of Science and Higher Education, Poland, grant no. N201274033
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.