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A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

100%

Androulakis G.

Studia Mathematica

1998

tom 127

nr 1

65-80

Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and there exists an isomorphically precisely norming set E for Y such that (*) is satisfied. As an application of this subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces we obtain a strengthening of a result of J. Elton, and an Orlicz-Pettis type result.

The Banach space S is complementably minimal and subsequentially prime

63%

Androulakis G., Schlumprecht T.

Studia Mathematica

2003

tom 156

nr 3

227-242

We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square. By the Pełczyński decomposition method it follows that every basic sequence in S which spans a space complemented in S has a subsequence which spans a space isomorphic to S (i.e. S is a subsequentially prime space).

Ograniczanie wyników

2 Studia Mathematica

2 Androulakis G.

1 Schlumprecht T.

1 2003

1 1998

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A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

The Banach space S is complementably minimal and subsequentially prime