共查询到20条相似文献,搜索用时 15 毫秒
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本文借助弱射影和弱透视的概念刻划了De Morgan代数的同余关系,由此得到了Kalman关于De Morgan代数次直不可约定理的一个新的证明并证明了一个完全分配的De Morgan代数的同余理想与同余关系一一对应的充要条件是L为弱可补的。 相似文献
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Cristina Draper Antonio Fernández López Esther García Miguel Gómez Lozano 《Journal of Algebra》2008,319(6):2372-2394
We define the socle of a nondegenerate Lie algebra as the sum of all its minimal inner ideals. The socle turns out to be an ideal which is a direct sum of simple ideals, and satisfies the descending chain condition on principal inner ideals. Every classical finite dimensional Lie algebra coincides with its socle, while relevant examples of infinite dimensional Lie algebras with nonzero socle are the simple finitary Lie algebras and the classical Banach Lie algebras of compact operators on an infinite dimensional Hilbert space. This notion of socle for Lie algebras is compatible with the previous ones for associative algebras and Jordan systems. We conclude with a structure theorem for simple nondegenerate Lie algebras containing abelian minimal inner ideals, and as a consequence we obtain that a simple Lie algebra over an algebraically closed field of characteristic 0 is finitary if and only if it is nondegenerate and contains a rank-one element. 相似文献
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Osamu Hatori 《Journal of Mathematical Analysis and Applications》2011,376(1):84-93
We prove that an isometry T between open subgroups of the invertible groups of unital Banach algebras A and B is extended to a real-linear isometry up to translation between these Banach algebras. While a unital isometry between unital semisimple commutative Banach algebras need not be multiplicative, we prove in this paper that if A is commutative and A or B are semisimple, then (T(eA))−1T is extended to an isometric real algebra isomorphism from A onto B. In particular, A−1 is isometric as a metric space to B−1 if and only if they are isometrically isomorphic to each other as metrizable groups if and only if A is isometrically isomorphic to B as a real Banach algebra; it is compared by the example of ?elazko concerning on non-isomorphic Banach algebras with the homeomorphically isomorphic invertible groups. Isometries between open subgroups of the invertible groups of unital closed standard operator algebras on Banach spaces are investigated and their general forms are given. 相似文献
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We show that weakly closed Jordan ideals in nest algebras on Banach spaces are associative ideals. The decomposability of
finite-rank operators in Jordan ideals and the commutants of bimodules are also investigated. 相似文献
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Positivity - This note is intended as an attempt at presenting some topological properties in cone metric spaces over Banach algebras. Moreover, the corresponding fixed point results are given. In... 相似文献
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The structure and properties of closed ideals of certain topological algebras of sections are studied. 相似文献
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Matej Brešar Victor S. Shulman Yuri V. Turovskii 《Integral Equations and Operator Theory》2010,67(2):279-300
The question of the existence of non-trivial ideals of Lie algebras of compact operators is considered from different points
of view. One of the approaches is based on the concept of a tractable Lie algebra, which can be of interest independently
of the main theme of the paper. Among other results it is shown that an infinite-dimensional closed Lie or Jordan algebra
of compact operators cannot be simple. Several partial answers to Wojtyński’s problem on the topological simplicity of Lie
algebras of compact quasinilpotent operators are also given. 相似文献
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We show that weakly closed Jordan ideals in nest algebras on Banach spaces are associative ideals. The decomposability of
finite-rank operators in Jordan ideals and the commutants of bimodules are also investigated.
Author’s address: J. Li and F. Lu, Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China
This research was supported by NNSFC (No. 10771154) and PNSFJ (NO. BK2007049). 相似文献
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Jun Tomiyama 《Acta Appl Math》2009,108(3):561-572
For the homeomorphism C*-algebra A(Σ) arising from a topological dynamical system Σ=(X,σ) where σ is a homeomorphism on an arbitrary compact Hausdorff space X, we first give detailed classification of its closed ideals into four classes. In case when X is a compact metric space, we then determine the conditions when the quotient algebras of A(Σ) become quasidiagonal. The case of A(Σ) itself was treated by M. Pimsner. 相似文献
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王建华 《数学物理学报(A辑)》2006,26(6):840-846
该文给出非自反Banach空间中一类超平面上度量投影的表达式.在近严格凸Banach空间中,研究了它们的连续性.对于对偶Banach空间X*,给出弱*闭子集上度量投影的一些连续性结果. 相似文献
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《数学学报》2016,(4)
正On Proximinality of Convex Sets in Superspaces Li Xin CHENG Zheng Hua LUO Wen ZHANG Ben Tuo ZHENG Abstract In this paper,we show that a closed convex subset C of a Banach space is strongly proximinal(proximinal,resp.)in every Banach space isometrically containing it if and only if C is locally(weakly,resp.)compact.As a consequence,it is proved that local compactness of C is also equivalent to that for every Banach space Y isometrically containing it,the metric 相似文献
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Let I be any index set. We consider the Banach algebra
\mathbb C e+ l2(I){\mathbb {C} e+ \ell^2(I)} with the Hadamard product, and prove that its Bass and topological stable ranks are both equal to 1. We also characterize
divisors, maximal ideals, closed ideals and closed principal ideals. For
I=\mathbb N{I=\mathbb {N}} we also characterize all prime z-ideals in this Banach algebra. 相似文献
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We provide a negative solution to a question of M. Rieffel who asked if the right and left topological stable ranks of a Banach
algebra must always agree. Our example is found amongst a class of nest algebras. We show that for many other nest algebras,
both the left and right topological stable ranks are infinite. We extend this latter result to Popescu’s non-commutative disc
algebras and to free semigroup algebras as well.
K. R. Davidson, L. W. Marcoux, H. Radjavi’s research was supported in part by NSERC (Canada).
An erratum to this article can be found at 相似文献
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Ferdinand Beckhoff 《Rendiconti del Circolo Matematico di Palermo》1997,46(3):451-464
The space Id(A) of closed two-sided ideals of a Banach algebra A carries the weak topology. IfA is separable Id(A) is expected to satisfy topological countability conditions. Some results concerning first and second countability are achieved. 相似文献
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V. N. Latyshev 《Moscow University Mathematics Bulletin》2011,66(3):110-113
A wide class of associative algebras admitting standard bases of ideals was introduced in previous papers of the author. They
are referred to as algebras with strong filtration. This class includes all known examples of associative algebras whose ideals
possess standard bases. It was proved by the author that the class of algebras with strong filtration is closed with respect
to direct sums and tensorial products. In this paper it is shown that this class is also closed with respect to free products
of algebras. 相似文献
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M. T. Karaev 《Functional Analysis and Its Applications》2018,52(1):1-8
We introduce Duhamel algebras and study their properties and applications. We prove that a Banach space of analytic functions on the unit disc that satisfy certain conditions is a Duhamel algebra and describe its closed ideals. These results substantially generalize and improve the main results of Wigley’s papers. Some other related questions are also discussed. 相似文献
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Mati Abel 《Central European Journal of Mathematics》2012,10(3):1054-1059
It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital
commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex. 相似文献