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ISSN 1088-6826(e) ISSN 0002-9939(p)

A hereditarily $\ell_1$ subspace of without the Schur property

Author(s): M. M. Popov
Journal: Proc. Amer. Math. Soc. 133 (2005), 2023-2028.
MSC (2000): Primary 46B20; Secondary 46E30
Posted: January 21, 2005
MathSciNet review: 2137868
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Abstract: Let $\infty > p_1 > p_2 > \cdots > 1$ . We construct an easily determined -symmetric basic sequence in $\Bigl( \sum\limits_{n=1}^{\infty} \oplus \ell_{p_n} \Bigr)_1$ , which spans a hereditarily $\ell_1$ subspace without the Schur property. An immediate consequence is the existence of hereditarily $\ell_1$ subspaces of without the Schur property.

References:

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Additional Information:

M. M. Popov
Affiliation: Department of Mathematics, Chernivtsi National University, str. Kotsjubyn'skogo 2, Chernivtsi, 58012 Ukraine
Email: popov@chv.ukrpack.net

DOI: 10.1090/S0002-9939-05-07758-0
PII: S 0002-9939(05)07758-0
Keywords: Schur property, the space $L_1$
Received by editor(s): August 24, 2003
Received by editor(s) in revised form: February 26, 2004
Posted: January 21, 2005
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2005, American Mathematical Society

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