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排序方式: 共有225条查询结果,搜索用时 578 毫秒
1.
Zhao Fang BAI Jin Chuan HOU 《数学学报(英文版)》2005,21(5):1167-1182
Let X be a (real or complex) Banach space with dimension greater than 2 and let B0(X) be the subspace of B(X) spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Ф on B0(X) which preserve nilpotent operators in both directions. In particular, if X is infinite-dimensional, we prove that Ф has the form either Ф(T) = cATA^-1 or Ф(T) = cAT'A^-1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T' denotes the adjoint of T. As an application of these results, we show that every additive surjective map on B(X) preserving spectral radius has a similar form to the above with |c| = 1. 相似文献
2.
Zhu Linsheng 《东北数学》1998,(1)
in this paper, the classification and realization of complete Lie algebras withcommutative nilpotent radicals are given. From this, some results on the radicals of thesecomplete Lie algebras are obtained. 相似文献
3.
Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied. 相似文献
4.
The main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will show that such a family contains a generic unfolding of a 4-dimensional nilpotent singularity of codimension 4. On the other hand, we will prove that in any generic unfolding Xμ of an n-dimensional nilpotent singularity of codimension n there are bifurcation curves of (n−1)-dimensional nilpotent singularities of codimension n−1 which are in turn generically unfolded by Xμ. Arguments conclude recalling that any generic unfolding of the 3-dimensional nilpotent singularity of codimension 3 exhibits strange attractors. 相似文献
5.
We completely characterize the global phase portraits in the Poincaré disk for all planar Hamiltonian vector fields with linear plus cubic homogeneous terms having a nilpotent saddle at the origin. 相似文献
6.
7.
In this paper, we study the explicit expansion of the first order Melnikov function near a double homoclinic loop passing through a nilpotent saddle of order m in a near-Hamiltonian system. For any positive integer , we derive the formulas of the coefficients in the expansion, which can be used to study the limit cycle bifurcations for near-Hamiltonian systems. In particular, for , we use the coefficients to consider the limit cycle bifurcations of general near-Hamiltonian systems and give the existence conditions for 10, 11, 13, 15 and 16 (11, 13 and 16, respectively) limit cycles in the case that the homoclinic loop is of cuspidal type (smooth type, respectively) and their distributions. As an application, we consider a near-Hamiltonian system with a nilpotent saddle of order 2 and obtain the lower bounds of the maximal number of limit cycles. 相似文献
8.
Let 1<p?2 and q be such that . It is well known that the norm of the Lp-Fourier transform of the additive group is , where . For a nilpotent Lie group G, we obtain the estimate , where m is the maximal dimension of the coadjoint orbits. Such a result was known only for some particular cases. 相似文献
9.
Fangyan Lu 《Journal of Mathematical Analysis and Applications》2003,284(1):127-143
Let X be a real or complex Banach space. Let and be two nest algebras on X. Suppose that φ is an additive bijective mapping from onto such that φ(A2)=φ(A)2 for every . Then φ is either a ring isomorphism or a ring anti-isomorphism. Moreover, if X is a real space or an infinite dimensional complex space, then there exists a continuous (conjugate) linear bijective mapping T such that either φ(A)=TAT−1 for every or φ(A)=TA∗T−1 for every . 相似文献
10.
Fei Xu 《Advances in Mathematics》2008,219(6):1872-1893
Let C be a small category and k a field. There are two interesting mathematical subjects: the category algebra kC and the classifying space |C|=BC. We study the ring homomorphism HH∗(kC)→H∗(|C|,k) and prove it is split surjective, using the factorization category of Quillen [D. Quillen, Higher algebraic K-theory I, in: Lecture Notes in Math., vol. 341, Springer-Verlag, Berlin, 1973, pp. 85-147] and certain techniques from functor cohomology theory. This generalizes the well-known theorems for groups and posets. Based on this result, we construct a seven-dimensional category algebra whose Hochschild cohomology ring modulo nilpotents is not finitely generated, disproving a conjecture of Snashall and Solberg [N. Snashall, Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc. 88 (3) (2004) 705-732]. 相似文献