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A strong uniform boundedness principle in Banach spaces

Author(s): Olav Nygaard
Journal: Proc. Amer. Math. Soc. 129 (2001), 861-863.
MSC (2000): Primary 46B20; Secondary 28A33
Posted: September 20, 2000
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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.

References:

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Mathematical Surveys 15 (1977). MR 56:12216
2.: V.P. FONF
Weakly extremal properties of Banach spaces.
Math. Notes 45 488-494 (1989). MR 90k:46032
3.: M.I. KADETS AND V.P. FONF
Two theorems on massiveness of a boundary in reflexive Banach space.
Funct. Anal. Appl. 17 77-78 (1983). MR 84j:46022
4.: G.L. SEEVER
Measures on F-spaces.
Trans. Amer. Math. Soc. 133 267-280 (1968). MR 37:1976

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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: 10.1090/S0002-9939-00-05607-0
PII: S 0002-9939(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
Posted: September 20, 2000
Communicated by: Dale Alspach
Copyright of article: Copyright 2000, American Mathematical Society


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