Automatique et corps différentiels.
Michel Fliess (1989)
Forum mathematicum
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Michel Fliess (1989)
Forum mathematicum
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Karl-Hermann Neeb (1997)
Forum mathematicum
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A. Eggert (1990)
Semigroup forum
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J. Alaminos, J. Extremera, Š. Špenko, A. R. Villena (2012)
Studia Mathematica
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Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.
John R. Faulkner (1994)
Forum mathematicum
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Y. Chae, Y. Lim (1994)
Semigroup forum
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Xiaofei Qi, Jinchuan Hou (2010)
Studia Mathematica
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A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A),B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a 𝒥-subspace lattice ℒ on a Banach space X satisfying dim K ≠ 2 whenever K ∈ 𝒥(ℒ), every linear map on ℱ(ℒ) (the subalgebra of all finite rank operators in the JSL algebra Alg ℒ) Lie derivable at zero is of the standard form A ↦ δ (A) + ϕ(A), where δ is a generalized derivation and ϕ is a center-valued linear map. A characterization of linear...
Rory Biggs, Claudiu C. Remsing (2015)
Communications in Mathematics
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We consider state space equivalence and feedback equivalence in the context of (full-rank) left-invariant control systems on Lie groups. We prove that two systems are state space equivalent (resp.~detached feedback equivalent) if and only if there exists a Lie group isomorphism relating their parametrization maps (resp. traces). Local analogues of these results, in terms of Lie algebra isomorphisms, are also found. Three illustrative examples are provided.
Chloup, Véronique (1995)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Baguis, P., Stavracou, T. (2002)
International Journal of Mathematics and Mathematical Sciences
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Hernández, I., Peniche, R. (2008)
International Journal of Mathematics and Mathematical Sciences
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Nijenhuis, A. (1996)
Archivum Mathematicum
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Jan Kubarski (1991)
Revista Matemática de la Universidad Complutense de Madrid
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R. L. Hudson, S. Pulmannová (2008)
Studia Mathematica
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Let 𝒯 be the Itô Hopf algebra over an associative algebra 𝓛 into which the universal enveloping algebra 𝓤 of the commutator Lie algebra 𝓛 is embedded as the subalgebra of symmetric tensors. We show that there is a one-to-one correspondence between deformations Δ[h] of the coproduct in 𝒯 and pairs (d⃗[h],d⃖[h]) of right and left differential maps which are deformations of the differential maps for 𝒯 [Hudson and Pulmannová, J. Math. Phys. 45 (2004)]. Corresponding to the multiplicativity...