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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
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.
References:
-
- 1.
- J. DIESTEL AND J.J. UHL, JR.
Vector measures.
American Mathematical Society, Providence.
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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