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A Lie derivation is called standard if it is a sum of a derivation and a linear map with image in the center vanishing on
commutators. In this paper we show that Lie derivations of a reflexive algebra on a Banach space are standard if is a nest, or has the non-trivial smallest element, or has the non-trivial greatest element.
This work was supported by NNSFC (No. 10771154) and PNSFJ (No. BK2007049). 相似文献
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Fangyan Lu 《Integral Equations and Operator Theory》2010,67(1):51-56
Let ${\mathcal L}Let L{\mathcal L} be a subspace lattice on a Banach space X and suppose that ú{L ? L: L- < X}=X{\vee\{L\in\mathcal L: L_- < X\}=X} or ${\land\{L_- : L \in \mathcal L, L>(0)\}=(0)}${\land\{L_- : L \in \mathcal L, L>(0)\}=(0)} . Then each Jordan derivation from AlgL{\mathcal L} into B(X) is a derivation. This result can apply to completely distributive subspace lattice algebras, J{\mathcal J} -subspace lattice algebras and reflexive algebras with the non-trivial largest or smallest invariant subspace. 相似文献
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令$\mathcal{L}$是一个满足$X_{-} \neq X$和$(0)_{+} \neq(0)$的Banach空间$X$上的子空间格.我们证明了从${\rm Alg}\,L$映到$B(X)$中的每个局部Lie $n$-导子是一个Lie $n$-导子. 相似文献
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A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献
7.
设A为Banach空间X中一自反代数使得在LatA中O ≠0且X_≠X,则A的每一环自同构¢(环反自同构φ)具有形式¢(A)=TAT^-1(φ(A)=TA^*T^-1),其中T:X→X(T:X^*→X)或为一有界线性双射算子或为一有界共轭线性性双射算子。特别地,¢和φ都是连续的。 相似文献
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本文证明了:Banach空间上完全分配格代数间的导子都是自动连续的;进而证明了套代数的可加导子是内的,套代数间的代数同构是自动连续的、空间的 相似文献
9.
Let ${\mathcal{L}}$ be a completely distributive subspace lattice on a Banach space and alg ${\mathcal{L}}$ the associated reflexive algebra. Suppose that the following $$\mbox{Condition A:}\dim(F/F\wedge F_-)\ne1\;\; \mbox{for all}\;\;F\in\mathcal{L}$$ holds; note that if ${\mathcal{L}}$ is an atomic Boolean subspace lattice, this condition means that every atom of ${\mathcal{L}}$ has dimension at least two. It is shown that every reflexive Jordan Alg ${\mathcal{L}}$ -module is an associative Alg ${\mathcal{L}}$ -module. We give an example which shows that if the Condition A is removed, then the conclusion is not necessarily true. Moreover, we prove that all reflexive Jordan ideals of Alg ${\mathcal{L}}$ are associative ideals in the case that no the Condition A is assumed. The same conclusions hold for weakly closed Jordan modules and weakly closed Jordan ideals if the rank one subalgebra of Alg ${\mathcal{L}}$ is weakly dense in Alg ${\mathcal{L}}$ . 相似文献
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§0. IntroductionLetLbeacollectionofclosedsubspacesofaHilbertspaceHcontaining{0}andHwhichformsacompletesubspacelatticeundertheoperations∧(intersection)and∨(closedlinearspan).WedenotebyalgLthealgebraofallboundedlinearoperatorswhichleaveallsubspacesinLi… 相似文献
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The Calabi-Yau spaces with SU(n) holonomy can be studied by the algebraic way through the integer lattice where one can construct the Newton reflexive polyhedra
or the Berger graphs. Our conjecture is that the Berger graphs can be directly related with the n-ary algebras. To find such algebras we study the n-ary generalization of the well-known binary norm division algebras,
, which helped to discover the most important “minimal” binary simple Lie groups, U(1), SU(2) and G(2). As the most important example, we consider the case n = 3, which gives the ternary generalization of quaternions (octonions), 3
n
, n = 2, 3, respectively. The ternary generalization of quaternions is directly related to the new ternary algebra (group) which
are related to the natural extensions of the binary su(3) algebra (SU(3) group). Using this ternary algebra we found the solution for the Berger graph: a tetrahedron.
“Why geniosis live so short? They wanna stay kids.”Alexey Dubrovski: On leave from JINR, Russia. Guennadi Volkov: On leave from PNPI, Russia. 相似文献
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设L是赋范线性空间上的子空间格,一个子空间是自反AlgL-模的充分必要条件被得到,当L是完全分配子空间格时,自反AlgL-模的二次交换子被描述,进而,本文引入V-生成子稠格,这是一种严格地包含了完全分配格和五角格的格类。当L是可换的V-生成子稠格时,模模交换子C(AlgL;M)和代数AlgLatM都被分解成直和,并且满足条件H~1(AlgL,B(H))=0的一阶上同调空间H~1(AlgL,M)被刻划。 相似文献
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Aleksey Yu. Karlovich 《Mathematische Nachrichten》1996,179(1):187-222
We consider singular integral operators with piecewise continuous coefficients on reflexive Orlicz spaces Lm(σ) which are generalizations of the Lebesgue spaces LP(σ), 1 < p < ∞. We suppose that σ belongs to a large class of Carleson curves, including curves with corners and cusps as well as curves that look locally like two logarithmic spirals scrolling up at the same point. For the singular integral operator associated with the Riemann boundary value problem with a piecewise continuous coefficient G, we establish a Fredholm criterion and an index formula in terms of the essential range of G complemented by spiralic horns depending on the Boyd indices of LM(σ) and contour properties. Our main result is a symbol calculus for the closed algebra of singular integral operators with piecewise continuous matrix - valued coefficients on LMn(σ). 相似文献
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A known characterization of the decomposability of polytopes is reformulated in a way which may be more computationally convenient,
and a more transparent proof is given. New sufficient conditions for indecomposability are then deduced, and illustrated with
some examples. 相似文献
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Michał Lasoń 《Discrete and Computational Geometry》2013,49(2):296-301
We prove that if a pure simplicial complex $\Delta $ of dimension $d$ with $n$ facets has the least possible number of $(d-1)$ -dimensional faces among all complexes with $n$ faces of dimension $d$ , then it is vertex decomposable. This answers a question of J. Herzog and T. Hibi. In fact, we prove a generalization of their theorem using combinatorial methods. 相似文献
16.
Houmem Belkhechine 《Discrete Mathematics》2017,340(12):2986-2994
Given a tournament , a module of is a subset of such that for and , if and only if . The trivial modules of are ,
and . The tournament is indecomposable if all its modules are trivial; otherwise it is decomposable. The decomposability index of , denoted by , is the smallest number of arcs of that must be reversed to make indecomposable. For , let be the maximum of over the tournaments with vertices. We prove that and that the lower bound is reached by the transitive tournaments. 相似文献
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E. G. Zelenyuk 《Ukrainian Mathematical Journal》1999,51(1):44-50
We prove that every countable Abelian group with finitely many second-order elements can be decomposed into countably many subsets that are dense in any nondiscrete group topology. Lutsk Industrial Institute, Lutsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 41–47, January, 1999. 相似文献
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Let V denote a finite dimensional vector space over a field K of characteristic 0, let Tn(V) denote the vector space whose elements are the K-valued n-linear functions on V, and let Sn(V) denote the subspace of Tn(V) whose members are the fully symmetric members of Tn(V). If n denotes the symmetric group on {1,2,…,n} then we define the projection by the formula , where Pσ : Tn(V) → Tn(V) is defined so that Pσ(A)(y1,y2,…,yn = A(yσ(1),yσ(2),…,yσ(n)) for each A?Tn(V) and yi?V, 1 ? i ? n. If , then x1?x2? … ?xn denotes the member of Tn(V) such that for each y1 ,2,…,yn in V, and x1·x2… xn denotes . If B? Sn(V) and there exists , such that B = x1·x2…xn, then B is said to be decomposable. We present two sets of necessary and sufficient conditions for a member B of Sn(V) to be decomposable. One of these sets is valid for an arbitrary field of characteristic zero, while the other requires that K = R or C. 相似文献
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We establish a decomposability criterion for linear sheaves on ℙ
n
. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙ
n
is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp. 相似文献