Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 34, 2009, 555-564
Mathematical Institute of the Czech Academy of Sciences
Zitná 25, 115 67, Prague 1, Czech Republic; fabian 'at' math.cas.cz
Universidad Politécnica de Valencia, Instituto de Matemática Pura y Aplicada
C/Vera, s/n. 46022 Valencia, Spain; algoncor 'at' doctor.upv.es
Universidad Politéecnica
de Valencia, Instituto de Matemática Pura y Aplicada
C/Vera, s/n. 46022 Valencia, Spain; vmontesinos 'at' mat.upv.es
Abstract. Using separable projectional resolutions of the identity, we provide a different proof of a result of Argyros and Mercourakis on the behavior of fundamental biorthogonal systems in weakly compactly generated (in short, WCG) Banach spaces. This result is used to discuss the example given by Argyros of a non-WCG subspace of a WCG space of the form C(K).
2000 Mathematics Subject Classification: Primary 46B26; Secondary 46B10, 46B15, 46B50.
Key words: Weakly compactly generated Banach spaces, biorthogonal systems, reflexivity, unconditional bases.
Reference to this article: M. Fabian, A. González and V. Montesinos: A note on biorthogonal systems in weakly compactly generated Banach spaces. Ann. Acad. Sci. Fenn. Math. 34 (2009), 555-564.
Copyright © 2009 by Academia Scientiarum Fennica