Premium
Limited Sets in C ( K )‐Spaces and Examples Concerning the Gelfand‐Phillips‐Property
Author(s) -
Schlumprecht Thomas
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921570105
Subject(s) - mathematics , property (philosophy) , unit sphere , pure mathematics , dual (grammatical number) , space (punctuation) , philosophy , epistemology , linguistics
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.