首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 31 毫秒
1.
Some rigidity results for non-commutative Bernoulli shifts   总被引:3,自引:0,他引:3  
We introduce the outer conjugacy invariants , for cocycle actions σ of discrete groups G on type II1 factors N, as the set of real numbers t>0 for which the amplification σt of σ can be perturbed to an action, respectively, to a weakly mixing action. We calculate explicitly and the fundamental group of σ, , in the case G has infinite normal subgroups with the relative property (T) (e.g., when G itself has the property (T) of Kazhdan) and σ is an action of G on the hyperfinite II1 factor by Connes–Størmer Bernoulli shifts of weights {ti}i. Thus, and coincide with the multiplicative subgroup S of generated by the ratios {ti/tj}i,j, while if S={1} (i.e. when all weights are equal), and otherwise. In fact, we calculate all the “1-cohomology picture” of σt,t>0, and classify the actions (σ,G) in terms of their weights {ti}i. In particular, we show that any 1-cocycle for (σ,G) vanishes, modulo scalars, and that two such actions are cocycle conjugate iff they are conjugate. Also, any cocycle action obtained by reducing a Bernoulli action of a group G as above on to the algebra pNp, for p a projection in N, p≠0,1, cannot be perturbed to a genuine action.  相似文献   

2.
Let T be an operator on a separable Banach space, and denote by σp(T) its point spectrum. We answer a question left open in (Israel J. Math. 146 (2005) 93–110) by showing that it is possible that be uncountable, yet Tn∞. We further investigate the relationship between the growth of sequences (nk) such that supkTnk<∞ and the possible size of .Analogous results are also derived for continuous operator semigroups (Tt)t0.  相似文献   

3.
We prove an index theorem for boundary value problems in Boutet de Monvel's calculus on a compact manifold X with boundary. The basic tool is the tangent semi-groupoid generalizing the tangent groupoid defined by Connes in the boundaryless case, and an associated continuous field of C*-algebras over [0,1]. Its fiber in =0, , can be identified with the symbol algebra for Boutet de Monvel's calculus; for ≠0 the fibers are isomorphic to the algebra of compact operators. We therefore obtain a natural map . Using deformation theory we show that this is the analytic index map. On the other hand, using ideas from noncommutative geometry, we construct the topological index map and prove that it coincides with the analytic index map.  相似文献   

4.
Let hp, 1<p<∞, be the best ℓp-approximation of the element from a proper affine subspace K of , hK, and let denote the strict uniform approximation of h from K. We prove that there are a vector and a real number a, 0a1, such that
for all p>1, where with γp=o(ap/p).  相似文献   

5.
Given two k element subsets , we give a quasi-linear algorithm to either find such that S=λT or prove that no such λ exists.This question is closely related to isomorphism testing of circulant graphs and has recently been studied in the literature.  相似文献   

6.
For a complex number α with let be the class of analytic functions f in the unit disk with f(0)=0 satisfying in , for some convex univalent function in . For any fixed , and we shall determine the region of variability V(z0,α,λ) for f(z0) when f ranges over the class
In the final section we graphically illustrate the region of variability for several sets of parameters z0 and α.  相似文献   

7.
This paper discusses the incompressible non-Newtonian fluid with rapidly oscillating external forces g(x,t)=g(x,t,t/) possessing the average g0(x,t) as →0+, where 0<0<1. Firstly, with assumptions (A1)–(A5) on the functions g(x,t,ξ) and g0(x,t), we prove that the Hausdorff distance between the uniform attractors and in space H, corresponding to the oscillating equations and the averaged equation, respectively, is less than O() as →0+. Then we establish that the Hausdorff distance between the uniform attractors and in space V is also less than O() as →0+. Finally, we show for each [0,0].  相似文献   

8.
On real-analytic recurrence relations for cardinal exponential B-splines   总被引:1,自引:0,他引:1  
Let LN+1 be a linear differential operator of order N+1 with constant coefficients and real eigenvalues λ1,…,λN+1, let E(ΛN+1) be the space of all C-solutions of LN+1 on the real line. We show that for N2 and n=2,…,N, there is a recurrence relation from suitable subspaces to involving real-analytic functions, and with if and only if contiguous eigenvalues are equally spaced.  相似文献   

9.
This study concerns the existence of positive solutions to the boundary value problemwhere ξi(0,1) with 0<ξ1<ξ2<<ξn-2<1, ai, bi[0,∞) with and . By applying the Krasnoselskii's fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general n-point boundary value problem.  相似文献   

10.
First and second kind paraorthogonal polynomials and their zeros   总被引:1,自引:0,他引:1  
Given a probability measure μ with infinite support on the unit circle , we consider a sequence of paraorthogonal polynomials hn(z,λ) vanishing at z=λ where is fixed. We prove that for any fixed z0supp(dμ) distinct from λ, we can find an explicit ρ>0 independent of n such that either hn or hn+1 (or both) has no zero inside the disk B(z0,ρ), with the possible exception of λ.Then we introduce paraorthogonal polynomials of the second kind, denoted sn(z,λ). We prove three results concerning sn and hn. First, we prove that zeros of sn and hn interlace. Second, for z0 an isolated point in supp(dμ), we find an explicit radius such that either sn or sn+1 (or both) have no zeros inside . Finally, we prove that for such z0 we can find an explicit radius such that either hn or hn+1 (or both) has at most one zero inside the ball .  相似文献   

11.
We strengthen the revised GCH theorem by showing, e.g., that for , for all but finitely many regular κ<ω, it holds that “λ is accessible on cofinality κ” in some weak sense (see below).As a corollary, λ=2μ=μ+>ω implies that the diamond holds on λ when restricted to cofinality κ for all but finitely many .We strengthen previous results on the black box and the middle diamond: previously it was established that these principles hold on for sufficiently large n; here we succeed in replacing a sufficiently large n with a sufficiently large n.The main theorem, concerning the accessibility of λ on cofinality κ, Theorem 3.1, implies as a special case that for every regular λ>ω, for some κ<ω, we can find a sequence such that , , and we can fix a finite set of “exceptional” regular cardinals θ<ω so that if Aλ satisfies |A|<ω, there is a pair-coloring so that for every -monochromatic BA with no last element, letting δ:=supB it holds that provided that is not one of the finitely many “exceptional” members of .  相似文献   

12.
V.V. Bavula  T.H. Lenagan   《Journal of Algebra》2008,320(12):4132-4155
Let K be an arbitrary field of characteristic zero, Pn:=K[x1,…,xn] be a polynomial algebra, and , for n2. Let σAutK(Pn) be given by
It is proved that the algebra of invariants, , is a polynomial algebra in n−1 variables which is generated by quadratic and cubic (free) generators that are given explicitly.Let σAutK(Pn) be given by
It is well known that the algebra of invariants, , is finitely generated (theorem of Weitzenböck [R. Weitzenböck, Über die invarianten Gruppen, Acta Math. 58 (1932) 453–494]), has transcendence degree n−1, and that one can give an explicit transcendence basis in which the elements have degrees 1,2,3,…,n−1. However, it is an old open problem to find explicit generators for Fn. We find an explicit vector space basis for the quadratic invariants, and prove that the algebra of invariants is a polynomial algebra over in n−2 variables which is generated by quadratic and cubic (free) generators that are given explicitly.The coefficients of these quadratic and cubic invariants throw light on the ‘unpredictable combinatorics’ of invariants of affine automorphisms and of SL2-invariants.  相似文献   

13.
We prove that if a vector-function f belongs to the Morrey space , with , n≥3, N≥2, λ]0,n−2], and u is the solution of the system
then Du belongs to the space , for any , provided the matrix of bounded measurable coefficients (Aij) has sufficiently small dispersion of the eigenvalues.  相似文献   

14.
Let I be a finite interval, , and 1p∞. Given a set M, of functions defined on I, denote by the subset of all functions yM such that the s-difference is nonnegative on I, τ>0. Further, denote by the Sobolev class of functions x on I with the seminorm x(r)Lp1. We obtain the exact orders of the Kolmogorov and the linear widths, and of the shape-preserving widths of the classes in Lq for s>r+1 and (r,p,q)≠(1,1,∞). We show that while the widths of the classes depend in an essential way on the parameter s, which characterizes the shape of functions, the shape-preserving widths of these classes remain asymptotically ≈n-2.  相似文献   

15.
This is the second in a series on configurations in an abelian category . Given a finite poset (I,), an (I,)-configuration (σ,ι,π) is a finite collection of objects σ(J) and morphisms ι(J,K) or in satisfying some axioms, where J,KI. Configurations describe how an object X in decomposes into subobjects.The first paper defined configurations and studied moduli spaces of (I,)-configurations in , using the theory of Artin stacks. It showed well-behaved moduli stacks of objects and configurations in exist when is the abelian category coh(P) of coherent sheaves on a projective scheme P, or mod- of representations of a quiver Q.Write for the vector space of -valued constructible functions on the stack . Motivated by the idea of Ringel–Hall algebras, we define an associative multiplication * on using pushforwards and pullbacks along 1-morphisms between configuration moduli stacks, so that is a -algebra. We also study representations of , the Lie subalgebra of functions supported on indecomposables, and other algebraic structures on .Then we generalize all these ideas to stack functions , a universal generalization of constructible functions, containing more information. When Exti(X,Y)=0 for all and i>1, or when for P a Calabi–Yau 3-fold, we construct (Lie) algebra morphisms from stack algebras to explicit algebras, which will be important in the sequels on invariants counting τ-semistable objects in .  相似文献   

16.
Let Ω be a region in the complex plane. In this paper we introduce a class of sesquianalytic reproducing kernels on Ω that we call B-kernels. When Ω is the open unit disk and certain natural additional hypotheses are added we call such kernels k Bergman-type kernels. In this case the associated reproducing kernel Hilbert space (k) shares certain properties with the classical Bergman space L2α of the unit disk. For example, the weighted Bergman kernels kβw(z)=(1−wz)β, 1β2 are Bergman-type kernels. Furthermore, for any Bergman-type kernel k one has H2 (k)L2a, where the inclusion maps are contractive, and Mζ, the operator of multiplication with the identity function ζ, defines a contraction operator on (k). Our main results about Bergman-type kernels k are the following two: First, once properly normalized, the reproducing kernel for any nontrivial zero based invariant subspace of (k) is a Bergman-type kernel as well. For the weighted Bergman kernels kβ this result even holds for all ζ-invariant subspace of index 1, i.e., whenever the dimension of /ζ is one. Second, if is any multiplier invariant subspace of (k), and if we set *= z , then Mζ is unitarily equivalent to Mζ acting on a space of *-valued analytic functions with an operator-valued reproducing kernel of the type
where V is a contractive analytic function V :  → ( ,  *), for some auxiliary Hilbert space . Parts of these theorems hold in more generality. Corollaries include contractive divisor, wandering subspace, and dilation theorems for all Bergman-type reproducing kernel Hilbert spaces. When restricted to index one invariant subspaces of (kβ), 1β2, our approach yields new proofs of the contractive divisor property, the strong contractive divisor property, and the wandering subspace theorems and inner–outer factorization. Our proofs are based on the properties of reproducing kernels, and they do not involve the use of biharmonic Green functions as had some of the earlier proofs.  相似文献   

17.
This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a class of degenerate and singular elliptic systems of the form
where Ω is a bounded domain with smooth boundary ∂Ω in , N2, and , , hi (i=1,2) are allowed to have “essential” zeroes at some points in Ω, (Fu,Fv)=F, and λ is a positive parameter. Our proofs rely essentially on the critical point theory tools combined with a variant of the Caffarelli–Kohn–Nirenberg inequality in [P. Caldiroli, R. Musina, On a variational degenerate elliptic problem, NoDEA Nonlinear Differential Equations Appl. 7 (2000) 189–199].  相似文献   

18.
Uzy Hadad   《Journal of Algebra》2007,318(2):607-618
Let R be a ring generated by l elements with stable range r. Assume that the group ELd(R) has Kazhdan constant 0>0 for some dr+1. We prove that there exist (0,l)>0 and , s.t. for every nd, ELn(R) has a generating set of order k and a Kazhdan constant larger than . As a consequence, we obtain for where n3, a Kazhdan constant which is independent of n w.r.t. generating set of a fixed size.  相似文献   

19.
Additive maps preserving Jordan zero-products on nest algebras   总被引:1,自引:0,他引:1  
Let and be nest algebras associated with the nests and on Banach Spaces. Assume that and are complemented whenever N-=N and M-=M. Let be a unital additive surjection. It is shown that Φ preserves Jordan zero-products in both directions, that is Φ(A)Φ(B)+Φ(B)Φ(A)=0AB+BA=0, if and only if Φ is either a ring isomorphism or a ring anti-isomorphism. Particularly, all unital additive surjective maps between Hilbert space nest algebras which preserves Jordan zero-products are characterized completely.  相似文献   

20.
Let E be a real reflexive Banach space with uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed and convex subset of E. Let T:KK be a strictly pseudo-contractive map and let L>0 denote its Lipschitz constant. Assume F(T){xK:Tx=x}≠0/ and let zF(T). Fix δ(0,1) and let δ* be such that δ*δL(0,1). Define , where δn(0,1) and limδn=0. Let {αn} be a real sequence in (0,1) which satisfies the following conditions: . For arbitrary x0,uK, define a sequence {xn}K by xn+1=αnu+(1−αn)Snxn. Then, {xn} converges strongly to a fixed point of T.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号