## Pacific Journal of Mathematics |

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### Contents

F Hiai M Ohya and M Tsukada Sufficiency KMS condition | 99 |

J Tomiyama See Inoue S Ota and J Tomiyama | 225 |

Tsukada See F Hiai M Ohya and M Tsukada | 250 |

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3-manifold abelian Amer assume automorphism Blaschke product block bounded C*-algebra closed coatoms commutes compact complete component condition constant contains continuous function convergence convex Corollary countable cycle defined denote derivation digraph disjoint division algebra element entropy equivalent exists fibration finite number follows given hB(a Hence Hilbert space homology homomorphism homotopy implies induces inequality infinite invariant subspaces irreducible isomorphic Ker(Aut kernel lattice Lemma Let f Let G Lie algebra Lie group Lie triple linear M/JM manifold Math maximal ideal measure metric space module multiplication neighborhood Neumann algebra notation obtain octonions operator partition polynomial prime profinite group projective proof of Theorem Proposition prove real division algebra realcompact resp result rings satisfies Sharkovsky's theorem Sidon set spectral sequence subalgebra subgroup subset summand Suppose theory topology UC(X vector Z)/torsion zero