Erratum to: Ball-covering property of Banach spaces

摘要: Though several conclusions of [1] (i.e., Lemma 4.2, Theorem 4.3, Corollary 4.4, 4.5 and 4.7) are true in a renorming sense using recent theorem either by V. Fonf C. Zanco [5] or L. Cheng, H. Shi W. Zhang [3], the proofs mentioned results use w∗-separability unit ball BX∗ dual space X ∗ under assumption that X∗ is w∗-separable w∗-sequential compactness with being w∗-angelic. However, as pointed out M. Fabian, does not imply [6] (see, also [8]), w ∗-separability entail w∗-angelic general. Recently, Kadets informed me an email closed ∞ endowed equivalent norm, defined mean natural norm quotient /c0 , such counterexample (see his review [4] Zentralblatt Math.: Zbl 1152.46010). Recall collection B open (closed) balls Banach said to be ball-covering if every contain origin covers sphere SX . We say has property, it admits countably many balls. Some authors consider ball-coverings balls, others — ones. Since countable union off contained almost same radius, we have following simple which says matter much two definitions one uses. Support Natural Science Foundation China, grant 10771175. Received September 4, 2009 revised form February 19, 2010