A note on Banach spaces with ℓ 1 -saturated duals

Denny H. Leung

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 3, page 515-517
  • ISSN: 0010-2628

Abstract

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It is shown that there exists a Banach space with an unconditional basis which is not c 0 -saturated, but whose dual is ℓ 1 -saturated.

How to cite

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Leung, Denny H.. "A note on Banach spaces with $\ell ^1$-saturated duals." Commentationes Mathematicae Universitatis Carolinae 37.3 (1996): 515-517. <http://eudml.org/doc/247933>.

@article{Leung1996,
abstract = {It is shown that there exists a Banach space with an unconditional basis which is not $c_0$-saturated, but whose dual is $\ell ^1$-saturated.},
author = {Leung, Denny H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {dual space; $\ell ^1$-saturated spaces; -saturated space; dual space; Lorenz space},
language = {eng},
number = {3},
pages = {515-517},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on Banach spaces with $\ell ^1$-saturated duals},
url = {http://eudml.org/doc/247933},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Leung, Denny H.
TI - A note on Banach spaces with $\ell ^1$-saturated duals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 3
SP - 515
EP - 517
AB - It is shown that there exists a Banach space with an unconditional basis which is not $c_0$-saturated, but whose dual is $\ell ^1$-saturated.
LA - eng
KW - dual space; $\ell ^1$-saturated spaces; -saturated space; dual space; Lorenz space
UR - http://eudml.org/doc/247933
ER -

References

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  1. Carothers N.L., Dilworth S.J., Subspaces of L p , q , Proc. Amer. Math. Soc. 104 (1988), 537-545. (1988) MR0962825
  2. Leung D.H., On c 0 -saturated Banach spaces, Illinois J. Math. 39 (1995), 15-29. (1995) MR1299646
  3. Lindenstrauss J., Tzafriri L., Classical Banach Spaces I, Springer-Verlag, 1977. Zbl0362.46013MR0500056
  4. Lindenstrauss J., Tzafriri L., Classical Banach Spaces II, Springer-Verlag, 1979. Zbl0403.46022MR0540367

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