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Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism. 相似文献
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Philip A. Ernst Wilfrid S. Kendall Gareth O. Roberts Jeffrey S. Rosenthal 《Stochastic Processes and their Applications》2019,129(2):355-380
Classical coupling constructions arrange for copies of the same Markov process started at two different initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two different Markov (or other stochastic) processes to remain equal for as long as possible, when started in the same state. We refer to this “un-coupling” or “maximal agreement” construction as MEXIT, standing for “maximal exit”. After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of MEXIT for Brownian motions with two different constant drifts. 相似文献
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《Indagationes Mathematicae》2021,32(6):1229-1239
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Wolfgang Bock Vyacheslav Futorny Mikhail Neklyudov 《Journal of Pure and Applied Algebra》2021,225(3):106535
A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is in analogue to the classical Jordan—Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrödinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra. 相似文献
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In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algeb... 相似文献
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《Wave Motion》2020
Working in the context of poroacoustics, we present new, physically relevant, explicit solutions to the Cauchy problem for the model we term the (1D) damped Riemann equation. The solitary waveforms that evolve from both Lorentzian (-smooth) and symmetric-exponential (-smooth) initial conditions are analyzed, the focus being on wave overturning and the evolution/structure of the shocks which develop thereafter. In addition to those for both the multi- and single-valued forms of each solution, expressions for the shock amplitude, velocity, and critical values of the physical parameters are derived/compared. Lastly, links to other areas of continuum physics, and possible follow-on investigations, are noted. 相似文献
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Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras. 相似文献