Satoshi Kawakami

The multiplicativity of the minimal index of simple c*-algebras

We show the multiplicativity of the minimal index for simple C*algebras. Although our proof is very short and elementary, it is also valid for subfactors, which was first shown by Kosaki and Longo (1992).

Commutative hypergroups associated with a hyperfield

In the present paper we introduce a commutative hypergroup associated with a hyperfield of a compact commutative hypergroup based on a discrete commutative hypergroup. Moreover we investigate the dual hyperfield and show the dual relation. As an application we study some hypergroups related to a pair of commutative hypergroups.

Hypergroups Related to a Pair of Compact Hypergroups

The purpose of the present paper is to investigate a hypergroup associated with irreducible characters of a compact hypergroup H and a closed subhypergroup H0 of H with jH=H0j < +1. The convolution of this hypergroup is introduced by inducing irreducible characters of H0 to H and by restricting irreducible characters of H to H0. The method of proof relies on the notion of an induced character and an admissible hypergroup pair.

Relative Entropy of a Fixed Point Algebra

The relative entropy H(M∣N) for a pair N ⊂M of finite von Neumann algebras was introduced and studied by M. Pimsner and S.Popa in [7]. One of their important results was to clarify the relationship between H(M∣N) and the Jones index [M : N] for a pair of finite factors ([2]). On the other hand, in [1], V. Jones succeeded in classifying actions of a finite group G on the hyperfinite type II1 factor R, up to conjugacy, associated with normal subgroups of G, characteristic invariants and inner invariants.