Abstract
We consider two types of conditions on an operator on a Banach space which ensure that it is the generator of a semigroup of contractions. First, S. Sakai's concept of commutative normal ∗-derivations of UHF algebras is generalized to “approximately commutative operators” on Banach spaces. Next we consider the situation in which the domain of the operator contains an increasing sequence of “approximately invariant subspaces,” and generalize results of A. Kishimoto and P. E. T. Jørgensen. A corollary is the existence of time development for two-dimensional quantum lattice models when the average surface energy per unit surface is uniformly bounded in the volume.
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