Let 0 be a locally compact abelian ordered group. We say that 0 has the extension property if every operator valued continuous positive definite function on an interval of 0 has a positive definite extension to the whole group and we say that 0 has the commutant lifting property if a natural extensi
Cohomology of topological groups and positive definite functions
β Scribed by A Guichardet
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 726 KB
- Volume
- 3
- Category
- Article
- ISSN
- 0047-259X
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π SIMILAR VOLUMES
Let G be a locally compact commutative group and let g and h be positive definite functions on G, which are not identically zero. We show that continuity of gh implies the existence of a character y of Gd (the discrete version of G) such that yg and y h are continuous. As corollary we get a special
Let f be a positive definite function on a locally compact abelian group G. In [3] we showed that measurability of 1 on an open neighbourhood of the zero implies measurability of f on G. As a main tool we used a result about the support of f [3, Th. I]. The aim of this note is to simplify the proof