Huzihiro Araki

On an inequality of Lieb and Thirring

AbstractThe following generalization of an inequality of Lieb and Thirring is proved:

On te Algebra of All Local Observables

Tr\{ b^{1 2} ab^{1 2} )^{qk} \} \leqslant Tr\{ (b^(q, 2) a^(q) b^(q 2)^k \}

Ground states of the

for all positive selfadjoint operatorsa andb and for positive numbersq>1 andk>0. More generally,

-model

Tr\varphi ((b^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} ab^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} )q) \leqslant Tr\varphi (b^{qk} a^q b^{{q \mathord{\left/ {\vphantom {q 2}} \right. \kern-\nulldelimiterspace} 2}} q)

INDECOMPOSABLE REPRESENTATIONS WITH INVARIANT INNER PRODUCT. A THEORY OF THE GUPTA-BLEULER TRIPLET

for any monotone increasing continuous function ϕ on (0, ∞) such that ϕ(0)=0 and ξ→ϕ(eξ) is convex.

On the homotopical significance of the type of von Neumann algebra factors

A one dimensional infinite quantum spin lattice with a finite range interaction is studied. The Gibbs state in the infinite volume limit is shown to exist as a primary state of a UHF algebra. The expectation value of any local observables in the state as well as the mean free energy depend analytically on the potential, showing no phase transition. The Gibbs state is an extremal KMS state.