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A strong uniform boundedness principle in Banach spaces


Author: Olav Nygaard
Journal: Proc. Amer. Math. Soc. 129 (2001), 861-863
MSC (2000): Primary 46B20; Secondary 28A33
DOI: https://doi.org/10.1090/S0002-9939-00-05607-0
Published electronically: September 20, 2000
MathSciNet review: 1626466
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Abstract: We discuss the term ``thick" set. With the help of this term we deduce a strong Uniform Boundedness Principle valid for all Banach spaces. As an application we give a new proof of Seever's theorem.


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Additional Information

Olav Nygaard
Affiliation: Deparment of Mathematics, Agder College, Tordenskjoldsgate 65, 4604 Kristian- sand, Norway
Email: Olav.Nygaard@hia.no

DOI: https://doi.org/10.1090/S0002-9939-00-05607-0
Keywords: Uniform boundedness principle, Seever's theorem
Received by editor(s): October 9, 1997
Received by editor(s) in revised form: May 13, 1998, and June 1, 1999
Published electronically: September 20, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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