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A characterization of conjugate WCG banach spaces

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Abstract

It is proved that a WCG Banach space X is isomorphic to a conjugate Banach space if and only if there exists a closed subspace V of its conjugate space X' with positive characteristic such that X possesses the following summability property with respect to V: For every bounded sequence in X there exists a regular essentially positive summability method A such that the A-means of the sequence are σ(X,V)-convergent in X. This extends a well-known theorem of Nishiura-Waterman [8] and yields an analogous characterization of quasi-reflexive spaces. Conjugate spaces of smooth Banach spaces can also be characterized by the above summability condition.

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  1. NWF I - Mathematik, Universität Regensburg, 8400, Regensburg, Germany

    Rudolf Brigola

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  1. Rudolf Brigola
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Brigola, R. A characterization of conjugate WCG banach spaces. Manuscripta Math 44, 95–102 (1983). https://doi.org/10.1007/BF01166076

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