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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On subsymmetric bases in Fréchet spaces


Author: Wieslaw Sliwa
Journal: Proc. Amer. Math. Soc. 135 (2007), 453-460
MSC (2000): Primary 46A35
Published electronically: August 8, 2006
MathSciNet review: 2255291
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Abstract: It is proved that any non-normable Fréchet space with a semi-symmetric absolute basis is isomorphic to the space $ \omega$ of all scalar sequences. A similar result is shown for quasi-homogeneous absolute bases. It is also proved that any nuclear Fréchet space with a semi-subsymmetric basis is isomorphic to $ \omega$.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08485-1
PII: S 0002-9939(06)08485-1
Keywords: Symmetric, semi-symmetric, semi-subsymmetric, quasi-homogeneous bases
Received by editor(s): October 6, 2004
Received by editor(s) in revised form: September 6, 2005
Published electronically: August 8, 2006
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society