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On Banach spaces with the Gelfand-Phillips property

✍ Scribed by Lech Drewnowski

Publisher
Springer-Verlag
Year
1986
Tongue
French
Weight
358 KB
Volume
193
Category
Article
ISSN
0025-5874

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Gelfand-Phillips Property in a Banach Sp
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In this paper (8, Z, p) will always denote a finite measure space and X a BA-NACH space. K ( p , 9) will denote the BANACH space of p-continuous X-valued measures G defined on L ? having relatively coinpact range, endowed with the semivariation norm (see Purpose of this note is to show that if X is

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## 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‐Phi

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## Abstract We consider a Gelfand‐Phillips type property for the weak topology. The main results that we obtain are (1) for certain Banach spaces, __E__^˜^~ϵ~ __F__ inherits this property from __E__ and __F__, and (2) the spaces __L__^p^(μ, __E__) have this property when __E__ does. A subset __A__