In this paper, using a power series methodology we describe a design procedure applicable to analytic nonlinear plants. Our technique is a generalization of the linear H theory. In contrast to previous work on this topic ([3], [14], [15]), we now are able to explicitly incorporate a causality constraint into the theory. In fact, we show that it is possible to reduce a causal optimal design prob...

Haag duality is a remarkable property in QFT stating that the commutant of algebra observables localized some region spacetime exactly associated to causally disconnected region. It strong condition on local structure and has direct consequences entanglement measures. was first shown hold for free scalar field causal diamonds by Araki 1964 later many authors different ways. In particular, Eckma...

We prove that an outer action of a locally compact group $G$ on full factor $M$ is automatically strictly outer, meaning the relative commutant in crossed product trivial. If moreover image automorphism Out closed, we remains full. obtain this result by proving inclusion has spectral gap property. Such results had only been proven for actions discrete groups and groups, using quite different me...

Kirchberg asked in 2004 whether the commutant of L(H) in its (norm) ultrapower is trivial. Assuming the Continnuum Hypothesis, we prove that the answer depends on the choice of the ultrafilter. Let H be a separable infinite dimensional complex Hilbert space, fixed throughout. The purpose of this paper is to prove that, assuming the Continnuum Hypothesis, the commutant of L(H) (the algebra of bo...

The relation between the lifting theorems due to Nagy-Foias and Cotlar-Sadosky is discussed. PRESENTATION. The Nagy-Foias commutant lifting theorem is a basic result in Operator Theory and its applications to interpolation problems. Its scope is shown in a fundamental book due to Foias and Frazho where we can read that “the work on the general framework of the commutant lifting theorem continue...

Suppose $\rho_1, \rho_2$ are two $\ell$-adic Galois representations of the absolute group a number field, such that algebraic monodromy one is connected and locally potentially equivalent at set places positive upper density. We classify pairs show up to twisting by some representation, it given pair which trivial other abelian. Consequently, assuming first representation has group, we obtain e...