共查询到20条相似文献,搜索用时 31 毫秒
1.
Xiaohong Cao 《Proceedings of the American Mathematical Society》2007,135(6):1701-1708
In this note, the relation between hypercyclic operator matrices (or supercyclic operator matrices) and the operator matrices which satisfy Weyl type theorems is discussed. Also, using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for for which a-Browder's theorem or a-Weyl's theorem holds.
2.
Mark E. Walker 《Transactions of the American Mathematical Society》2004,356(7):2569-2648
We present a novel proof of Thomason's theorem relating Bott inverted algebraic -theory with finite coefficients and étale cohomology for smooth varieties over algebraically closed ground fields. Our proof involves first introducing a new theory, which we term algebraic -homology, and proving it satisfies étale descent (with finite coefficients) on the category of normal, Cohen-Macaulay varieties. Then, we prove algebraic -homology and algebraic -theory (each taken with finite coefficients) coincide on smooth varieties upon inverting the Bott element.
3.
Jyh-Haur Teh 《Transactions of the American Mathematical Society》2008,360(6):3263-3285
We generalize the Harnack-Thom theorem to relate the ranks of the Lawson homology groups with -coefficients of a real quasiprojective variety with the ranks of its reduced real Lawson homology groups. In the case of zero-cycle group, we recover the classical Harnack-Thom theorem and generalize the classical version to include real quasiprojective varieties. We use Weil's construction of Picard varieties to construct reduced real Picard groups, and Milnor's construction of universal bundles to construct some weak models of classifying spaces of some cycle groups. These weak models are used to produce long exact sequences of homotopy groups which are the main tool in computing the homotopy groups of some cycle groups of divisors. We obtain some congruences involving the Picard number of a nonsingular real projective variety and the rank of its reduced real Lawson homology groups of divisors.
4.
Kyriakos Kontostathis 《Mathematical Logic Quarterly》1992,38(1):189-195
We formulate an abstract version of the finite injury method in the form of the Baire category theorem. The theorem has the following corollaries: The Friedberg-Muchnik pair of recursively enumerable degrees, the Sacks splitting theorem, the existence of a minimal degree below 0′ and the Shoenfield jump theorem. 相似文献
5.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(6):719-722
We consider arithmetic varieties endowed with an action of the group scheme of n-th roots of unity and we define equivariant arithmetic K0-theory for these varieties. We then state a Riemann-Roch theorem for the natural transformation of equivariant arithmetic K0 -theory induced by the restriction to the fixed point scheme and we show that it implies a version of Bismut's conjecture of an equivariant arithmetic Riemann-Roch theorem. 相似文献
6.
We give a computation of the K-groups of Grassmannians and flag varieties over an arbitrary Noetherian base scheme. We also compute the K-groups of forms of Grassmannians and flag varieties associated to a sheaf of Azumaya algebras. One ingredient in the computation is the extension of the Bott theorem on the cohomology of line bundles on the flag variety (over Q) to a K
0-Bott theorem valid over arbitrary Noetherian base schemes.Partially supported by the NSF. 相似文献
7.
本文给出了关于L0- 线性函数的Hahn-Banach 扩张定理的几何形式并证明这个几何形式等价于它的代数形式. 进一步, 我们利用这个几何形式给出了随机局部凸模中熟知的基本分离定理的一个新的且简单的证明. 最后, 利用这个分离定理, 我们同时在两种拓扑 —(ε, λ)- 拓扑和局部L0- 凸拓扑下证明了随机赋范模中的Goldstine-Weston 稠密性定理, 并举出一个反例说明在局部L0- 凸拓扑下如果随机赋范模不具有可数连接性质, 则Goldstine-Weston 稠密性定理不一定成立. 相似文献
8.
We prove the existence of rational points on singular varieties over finite fields arising as degenerations of smooth proper
varieties with trivial Chow group of 0-cycles. We also obtain congruences for the number of rational points of singular varieties
appearing as fibres of a proper family with smooth total and base space and such that the Chow group of 0-cycles of the generic
fibre is trivial. In particular this leads to a vast generalization of the classical Chevalley-Warning theorem. The above
results are obtained as special cases of our main theorem which can be viewed as a relative version of a theorem of H. Esnault
on the number of rational points of smooth proper varieties over finite fields with trivial Chow group of 0-cycles. 相似文献
9.
A∈B(H)称为是一个Drazin可逆的算子,若A有有限的升标和降标.用σ_D(A)={λ∈C:A-λI不是Drazin可逆的)表示Drazin谱集.本文证明了对于Hilbert空间上的一个2×2上三角算子矩阵M_C=■,从σ_D(A)∪σ_D(G)到σ_D(M_C)的道路需要从前面子集中移动σ_D(A)∩σ_D(B)中一定的开子集,即有等式:σ_D(A)∪σ_D(B)=σ_D(M_C)∪G,其中G为σ_D(M_C)中一定空洞的并,并且为σ_D(A)∪σ_D(B)的子集.2×2算子矩阵不一定满足Weyl定理,利用Drazin谱,我们研究了2×2上三角算子矩阵的Weyl定理,Browder定理,a-Weyl定理和a-Browder定理. 相似文献
10.
刘玉玲 《数学的实践与认识》2007,37(16):168-173
通过利用Krasnosel′skii不动点定理的扩充定理,对于一类含导数的非线性二阶m-点边值问题(1.1)+(1.2)u″(t)+f(t,u(t),u′(t))=0,0相似文献
11.
12.
13.
Martine C.B. Reurings 《Linear algebra and its applications》2006,418(1):292-311
In this paper we will give necessary and sufficient conditions under which a map is a contraction on a certain subset of a normed linear space. These conditions are already well known for maps on intervals in R. Using the conditions and Banach’s fixed point theorem we can prove a fixed point theorem for operators on a normed linear space. The fixed point theorem will be applied to the matrix equation X = In + A∗f(X)A, where f is a map on the set of positive definite matrices induced by a real valued map on (0, ∞). This will give conditions on A and f under which the equation has a unique solution in a certain set. We will consider two examples of f in detail. In one example the application of the fixed point theorem is the first step in proving that the equation has a unique positive definite solution under the conditions on A. 相似文献
14.
We prove the following theorem. Let m and n be any positive integers with mn, and let
be a subset of the n-dimensional Euclidean space
n
. For each i=1, . . . , m, there is a class
of subsets M
i
j
of
Tn
. Assume that
for each i=1, . . . , m, that M
i
j
is nonempty and closed for all i, j, and that there exists a real number B(i, j) such that
and its jth component
xjB(i, j)
imply
. Then, there exists a partition
of {1, . . . , n} such that
for all i and
We prove this theorem based upon a generalization of a well-known theorem of Birkhoff and von Neumann. Moreover, we apply this theorem to the fair allocation problem of indivisible objects with money and obtain an existence theorem. 相似文献
15.
The purpose of this paper is to establish some new matching theorems in G-convex spaces and, as applications, to obtain some new fixed point theorems, section theorems and a minimax theorem in G-convex spaces. The results presented in this paper improve and generalize the corresponding results in [1], [2], [3], [4], [5], [7], [8], [9], [10], [11] and [12]. 相似文献
16.
一类Φ-Laplacian多点边值问题的可解性 总被引:1,自引:0,他引:1
代祖华 《数学的实践与认识》2005,35(4):188-196
获得了一类Φ-Laplacian多点边值问题((u′) )′=f (t,u,u′) ,0 相似文献
17.
Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds 总被引:6,自引:0,他引:6
MA Jipu 《中国科学A辑(英文版)》2000,43(12):1233-1237
Applications of locally fine property for operators are further developed. LetE andF be Banach spaces andF:U(x
0)⊂E→F be C1 nonlinear map, whereU (x
0) is an open set containing pointx
0∈E. With the locally fine property for Frechet derivativesf′(x) and generalized rank theorem forf′(x), a local conjugacy theorem, i. e. a characteristic condition forf being conjugate tof′(x
0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced
calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives
rise to a generalized principle for constructing Banach submanifolds. 相似文献
18.
Rank theorems of operators between Banach spaces 总被引:13,自引:0,他引:13
MA Jipu 《中国科学A辑(英文版)》2000,43(1):1-5
Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis. 相似文献
19.
Claude-Alain Faure 《Geometriae Dedicata》2002,90(1):145-151
The following version of the fundamental theorem is proved: Let V, W be vector spaces and g: P(V)\E P(W) a morphism between the associated projective spaces. If the image of g is not contained in a line, then there exists a semilinear map f: V W which induces g. The difficulty lies in the fact that the homomorphism of division rings associated to the map f can be nonsurjective. As an application, a short proof of Wigner's theorem is also proposed. 相似文献
20.
In a lecture in Kazan (1977), Goncharov dubbed a number of problems regarding the classification of computable members of various classes of structures. Some of the problems seemed likely to have nice answers, while others did not. At the end of the lecture, Shore asked what would be a convincing negative result. The goal of the present article is to consider some possible answers to Shore's question. We consider structures of some computable language, whose universes are computable sets of constants. In measuring complexity, we identify with its atomic diagram D(), which, via the Gödel numbering, may be treated as a subset of . In particular, is computable if D() is computable. If K is some class, then Kc denotes the set of computable members of K. A computable characterization for K should separate the computable members of K from other structures, that is, those that either are not in K or are not computable. A computable classification (structure theorem) should describe each member of Kc up to isomorphism, or other equivalence, in terms of relatively simple invariants. A computable non-structure theorem would assert that there is no computable structure theorem. We use three approaches. They all give the correct answer for vector spaces over Q, and for linear orderings. Under all of the approaches, both classes have a computable characterization, and there is a computable classification for vector spaces, but not for linear orderings. Finally, we formulate some open problems. 相似文献