Algebras of observables with continuous representations of symmetry groups
β Scribed by Karl Kraus
- Publisher
- Springer
- Year
- 1968
- Tongue
- English
- Weight
- 841 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0010-3616
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π SIMILAR VOLUMES
We consider the following class of unitary representations ? of some (real) Lie group G which has a matched pair of symmetries described as follows: (i) Suppose G has a period-2 automorphism {, and that the Hilbert space H(?) carries a unitary operator J such that J?=(? b {) J (i.e., selfsimilarity)
We prove that if \(T\) is a strongly based continuous bounded representation of a locally compact abelian group \(G\) on a Banach Space \(X\), and if the spectrum of \(T\) is countable, then the Banach algebra generated by \(f(T)=\int_{G} f(g) T(g) d g\), \(f \in L^{1}(G)\), is semisimple. 1994 Acad