共查询到20条相似文献,搜索用时 0 毫秒
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Let 𝒜 be a unital Banach algebra and ? be a unital 𝒜-bimodule. We show that if δ is a linear mapping from 𝒜 into ? satisfying δ(ST)?=?δ(S)T?+Sδ(T) for any S, T?∈?𝒜 with ST?=?W, where W is a left or right separating point of ?, then δ is a Jordan derivation. Also, it is shown that every linear mapping h from 𝒜 into a unital Banach algebra ? which satisfies h(S)h(T)?=?h(ST) for any S,?T?∈?𝒜 with ST?=?W is a Jordan homomorphism if h(W) is a separating point of ?. 相似文献
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Janusz Zieliński 《Central European Journal of Mathematics》2010,8(4):780-785
Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations. 相似文献
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We prove that every weak-local derivation on a C*-algebra is continuous, and the same conclusion remains valid for weak*-local derivations on von Neumann algebras. We further show that weak-local derivations on C*-algebras and weak*-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal*-automorphism with our notions of extreme-strong-local derivations and automorphisms. 相似文献
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In [2, Theorem 3], Bell and Kappe proved that if d is a derivation of a prime ring R which acts as a homomorphism or an anti-homomorphism on a nonzero right ideal I of R, then d = 0 on R. In the present paper our objective is to extend this result to Lie ideals. The following result is proved: Let R be a 2-torsion free prime ring and U a nonzero Lie ideal of R such that u 2 ∈ U, for all u ∈ U. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U ?Z(R). 相似文献
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Let 1≦m≦4 be a fixed integer and let f:X→Y be a mapping with X, Y two vector spaces. The functional equation (1.1) is said to be additive if m=1, quadratic if m=2, cubic if m=3 and quartic if m=4, respectively. For convenience, a solution of (1.1) will be called an m-mapping. Let $\mathcal{A}$ , $\mathcal{B}$ be two algebras. An m-mapping $f\colon \mathcal{A} \to \mathcal{B}$ will be called m-derivation if the equality f(xy)=x m f(y)+f(x)y m is fulfilled for all $x,y\in \mathcal{A}$ . In this paper, we use a fixed point method to prove the stability and hyperstability of m-derivations on Banach algebras. 相似文献
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Vincenzo de Filippis 《数学学报(英文版)》2009,25(12):1965-1974
Let R be a prime ring, L a non-central Lie ideal of R and g a non-zero generalized derivation of R. If g acts as a Jordan homomorphism on L, then either g(x) = x for all x ∈ R, or char(R) = 2, R satisfies the standard identity s4(x1, x2, x3, x4), L is commutative and u2 ∈ Z(R), for any u C L. We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set [I, I], where I is a non-zero right ideal of R. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2008,13(1):106-113
This is a report on the current state of affairs in the rigorous microscopic foundations of the Vlasov regime of kinetic theory. 相似文献
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《Journal of the Egyptian Mathematical Society》2014,22(3):327-329
Let R be a prime ring with characteristic different from 2 and L be a Lie ideal of R. In this paper, we characterize generalized left derivation, which acts as a homomorphisms or an anti-homomorphisms on L. 相似文献
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Madjid Eshaghi Gordji Norouz Ghobadipour Ali Ebadian 《Rendiconti del Circolo Matematico di Palermo》1936,60(1-2):125-137
In this paper, we will apply a fixed point method for proving the generalized Hyers–Ulam–Rassias stability of the partial derivations for Jensen type n-variable functional equations. 相似文献
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V. I. Kachalov 《Differential Equations》2014,50(1):8-14
We present an algebraic approach to the theory of ordinary differential equations and indicate a method for constructing first integrals of such equations. 相似文献
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David London 《Linear and Multilinear Algebra》2013,61(3):179-189
Let L be a linear transformation on the set of all n×n matrices over an algebraically closed field of characteristic 0. It is shown that if AB=BA implies L(A)L(B)=L(B)L(A) and if either L is nonsingular or the implication in the hypothesis can also be reversed, then L is a sum of a scalar multiple of a similarity transformation and a linear functional times the identity transformation. 相似文献
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Let Alg? be a reflexive algebra on a Hilbert space H. We say that a linear map δ: Alg??→?Alg? is derivable at Ω?∈?Alg? if δ(A)B?+?Aδ(B)?=?δ(Ω) for every A, B?∈?Alg? with AB?=?Ω. In this article, we give a necessary and sufficient condition for a map δ on Alg? to be derivable at Ω. In particular, we show that every linear map δ derivable at Ω?≠?0 from an irreducible CDC algebra (in particular, a nest algebra) into itself is a derivation. Moreover, if Alg? is a CSL algebra, and if for some nontrivial projection P?∈??, PΩP and (I???P)Ω(I???P) are left or right separating points in PAlg?P and (I???P)Alg?(I???P) respectively, then a linear map δ on Alg? is derivable at Ω if and only if δ is a derivation. 相似文献
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Joe Masaro 《Linear algebra and its applications》2010,432(6):1578-1594
For a real, Hermitian, or quaternion normal random matrix Y with mean zero, necessary and sufficient conditions for a quadratic form Q(Y) to have a Wishart-Laplace distribution (the distribution of the difference of two independent central Wishart Wp(mi,Σ) random matrices) are given in terms of a certain Jordan algebra homomorphism ρ. Further, it is shown that {Qk(Y)} is independent Laplace-Wishart if and only if in addition to the aforementioned conditions, the images ρk(Σ+) of the Moore-Penrose inverse Σ+ of Σ are mutually orthogonal: ρk(Σ+)ρ?(Σ+)=0 for k≠?. 相似文献