Limited Sets in C(K)-Spaces and Examples Concerning the Gelfand-Phillips-Property

✍ Scribed by Thomas Schlumprecht

• Publisher: John Wiley and Sons
• Year: 1992
• Tongue: English
• Weight: 727 KB
• Volume: 157
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19921570105

✦ Synopsis

Abstract

In this paper we give criteria for limitedness in C(K)‐spaces and discuss the Gelfand‐Phillips‐property. We show that the Gelfand‐Phillips‐property is not a three‐space‐property, that l~1~ ⊄ X does not imply the Gelfand‐Phillips‐property of X and that the Gelfand‐Phillips‐property of a space X does not imply that the dual unit ball contains a w*‐sequentially precompact subset which norms X up to a constant.