Vol. 40, No. 2, 1972

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Covariant representations of infinite tensor product algebras

Richard Howard Herman and Michael Charles Reed

Vol. 40 (1972), No. 2, 311–326

In this paper myriad covariant representations of a class of C-algebras and automorphism groups are constructed. The Hilbert spaces on which the representations are realized have an unusual structure: they are direct integrals of measurable families H() of Hilbert spaces over the spectrum of an abelian subalgebra of the C-algebra; the fibre spaces H(ζ) are (in general) different separable subspaces of inseparable infinite tensor product spaces. The representors of the algebra and the unitary representors of the group do not decompose but act both in the fibres and on the underlying spectrum. Cases covered by this construction include the quasifree automorphisms of the Clifford algebra which leave a given basis fixed and the automorphism corresponding to charge conjugation.

Mathematical Subject Classification 2000
Primary: 46L05
Secondary: 46M05
Received: 17 December 1970
Published: 1 February 1972
Richard Howard Herman
Michael Charles Reed