JEDNOSTKA NAUKOWA KATEGORII A+

A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

Tom 127 / 1998

G. Androulakis Studia Mathematica 127 (1998), 65-80 DOI: 10.4064/sm-127-1-65-80

Streszczenie

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.

Autorzy

  • G. Androulakis

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek