Transfinite duals of quasireflexive Banach spaces
Author:
Steven F. Bellenot
Journal:
Trans. Amer. Math. Soc. 273 (1982), 551-577
MSC:
Primary 46B10
DOI:
https://doi.org/10.1090/S0002-9947-1982-0667160-2
MathSciNet review:
667160
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Abstract | References | Similar Articles | Additional Information
Abstract: The transfinite duals of a space with a neighborly basis are constructed until they become nonseparable. Let be the first ordinal
so that
is nonseparable. It is shown that if
is nonreflexive,
(this is best possible) and that
. A quasireflexive space
is constructed so that
is isomorphic to
and no basic sequence in
is equivalent to a neighborly basis. It is shown that the
th dual of James space and James function space are isomorphic to subspaces of one another. Also, perhaps of interest on its own, a reflexive space with a subsymmetric basis is constructed whose inversion spans a nonreflexive space.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1982-0667160-2
Keywords:
Neighborly,
equal signs additive,
invariant under spreading,
quasireflexive,
transfinite duals,
separable and nonseparable,
James space,
inversion of a basis
Article copyright:
© Copyright 1982
American Mathematical Society