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The unit ball of the Hilbert space in its weak topology
Author(s):
Antonio
Avilés
Journal:
Proc. Amer. Math. Soc.
135
(2007),
833-836.
MSC (2000):
Primary 46B50, 46B26, 46C05, 54B30, 54D15
Posted:
September 15, 2006
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Abstract:
We show that the unit ball of  in its weak topology is a continuous image of  , and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when  is uncountable.
References:
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Additional Information:
Antonio
Avilés
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo (Murcia), Spain
Address at time of publication:
Equipe de Logique Mathematique, Université de Paris 7, Place Jussieu, 2, 75251 Paris, France
Email:
avileslo@um.es
DOI:
10.1090/S0002-9939-06-08527-3
PII:
S 0002-9939(06)08527-3
Keywords:
Uniform Eberlein compact,
polyadic space,
$\ell_p$ spaces,
Hilbert space,
weak topology,
equivalent norm
Received by editor(s):
March 2, 2005
Received by editor(s) in revised form:
October 19, 2005
Posted:
September 15, 2006
Additional Notes:
The author was supported by an FPU grant of MEC of Spain.
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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