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1.
Let H olenote a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator T ∈ L(H) is said to be strongly irreducible if T does not commute with any nontrivial idempotent. Herrero and Jiang showed that the norm-closure of the class of all strongly irreducible operators is the class of all operators with connected spectrum. This result can be considered as an approximate inverse of the Riesz decomposition theorem. In the paper, we give a more precise charact... 相似文献
2.
Chaohui ZHANG? 《数学年刊B辑(英文版)》2008,29(1):85-94
It is well known that certain isotopy classes of oseudo-Anosov maos on a Riemann surface S of non-excluded type can be defined through Dehn twists tα and tβ along simple closed geodesics α and β on S,respectively. Let G be the corresponding Fuchsian group acting on the hyperbolic plane H so that H/G≌S.For any point α∈S,define S = S/{α}.In this article, the author gives explicit parabolic elements of G from which he constructs pseudo-Anosov classes on S that can be projected to a given pseudo-Anosov class on S obtained from Thurston's construction. 相似文献
3.
In this paper we mainly study the derivations for even part of the finite-dimensional odd Hamiltonian superalgebra HO over a field of prime characteristic. We first give the generating set of the even part g of HO. Then we compute the derivations from g into the even part m of the generalized Witt superalgebra. Finally, we determine the derivation algebra and outer derivation algebra of and the dimension formulas. In particular, the first cohomology groups H^1(g;m) and H^1(g;g) are determined. 相似文献
4.
WenMing Wu 《中国科学A辑(英文版)》2008,51(11):2081-2088
Given the hyperbolic measure dxdy/y
2 on the upper half plane ℍ, the rational actions of PSL2(ℝ) on ℍ induces a continuous unitary representation α of this group on the Hilbert space L
2(ℍ, dxdy/y
2). Supposing that = {M
f
: f ∈ L
∞ (ℍ, dxdy/y
2)}, we show that the crossed product is of type I. In fact, the crossed product is *-isomorphic to the von Neumann algebra , where is the abelian group von Neumann algebra generated by the left regular representation of K.
This work was supported by the Youth Foundation of Sichuan Education Department of China (Grant No. 2003B017) 相似文献
5.
Friedrich Haslinger 《Czechoslovak Mathematical Journal》2008,58(4):1247-1256
We prove that compactness of the canonical solution operator to restricted to (0, 1)-forms with holomorphic coefficients is equivalent to compactness of the commutator
defined on the whole L
(0,1)2(Ω), where is the multiplication by and is the orthogonal projection of L
(0,1)2(Ω) to the subspace of (0, 1) forms with holomorphic coefficients. Further we derive a formula for the -Neumann operator restricted to (0, 1) forms with holomorphic coefficients expressed by commutators of the Bergman projection
and the multiplications operators by z and .
Partially supported by the FWF grant P19147-N13. 相似文献
6.
Niels Grønbæk 《Proceedings Mathematical Sciences》2008,118(2):235-243
Let be a Banach algebra and let X be a Banach -bimodule. In studying (,X) it is often useful to extend a given derivation D: → X to a Banach algebra containing as an ideal, thereby exploiting (or establishing) hereditary properties. This is usually done using (bounded/unbounded) approximate
identities to obtain the extension as a limit of operators b ↦ D(ba) − b.D(a), a ε in an appropriate operator topology, the main point in the proof being to show that the limit map is in fact a derivation.
In this paper we make clear which part of this approach is analytic and which algebraic by presenting an algebraic scheme
that gives derivations in all situations at the cost of enlarging the module. We use our construction to give improvements
and shorter proofs of some results from the literature and to give a necessary and sufficient condition that biprojectivity
and biflatness is inherited to ideals. 相似文献
7.
JianMing Chang 《中国科学A辑(英文版)》2009,52(8):1717-1722
Let be a family of meromorphic functions in a plane domain D, and a and b be finite non-zero complex values such that . If for and , then is normal. We also construct a non-normal family of meromorphic functions in the unit disk Δ={|z|<1} such that for every and in Δ, where m is a given positive integer. This answers Problem 5.1 in the works of Gu, Pang and Fang.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10671093, 10871094) and the Natural Science
Foundation of Universities of Jiangsu Province of China (Grant No. 08KJB110001), the Qing Lan Project of Jiangsu, China and
the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry 相似文献
8.
We study the set of infinitely differentiable periodic functions in terms of generalized -derivatives defined by a pair of sequences ψ
1 and ψ
2. It is shown that every function ƒ from the set has at least one derivative whose parameters ψ
1 and ψ
2 decrease faster than any power function and, at the same time, for any function ƒ ∈ different from a trigonometric polynomial, there exists a pair ψ whose parameters ψ
1 and ψ
2 have the same rate of decrease and for which the -derivative no longer exists.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1399–1409, October, 2007. 相似文献
9.
The main purpose of this paper is to prove the following result. Let H be a complex Hilbert space, let (H) be the algebra of all bounded linear operators on H, and let (H) ⊂ (H) be a standard operator algebra which is closed under the adjoint operation. Suppose that T: (H) → (H) is a linear mapping satisfying T(AA* A) = T(A)A* A − AT(A*)A + AA*T(A) for all A ∈ (H). Then T is of the form T(A) = AB + BA for all A ∈ (H), where B is a fixed operator from (H). A result concerning functional equations related to bicircular projections is proved
相似文献
10.
In the 1970's,Folland and Stein studied a family of subelliptic scalar operators L_λwhich arise naturally in the(?)_b-complex.They introduced weighted Sobolev spaces as the natural spaces for this complex,and then obtained sharp estimates for(?)b in these spaces using integral kernels and approximate inverses.In the 1990's,Rumin introduced a differential complex for compact contact manifolds,showed that the Folland-Stein operators are central to the analysis for the corresponding Laplace operator,and derived the necessary estimates for the Laplacian from the Folland Stein analysis. In this paper,we give a self-contained derivation of sharp estimates in the anisotropic Folland-Stein spaces for the operators studied by Rumin using integration by parts and a modified approach to bootstrapping. 相似文献
11.
Sigurd Angenent 《数学学报(英文版)》2008,24(12):1949-1952
Given a symmetric Finsler metric on T^2 whose geodesic flow has zero topological entropy, we show that the lift in the universal covering R^2 →T^2 of any closed geodesic on T^2 must be an embedded curve in R^2. 相似文献
12.
An (n,k)-affine source over a finite field is a random variable X = (X
1,..., X
n
) ∈ , which is uniformly distributed over an (unknown) k-dimensional affine subspace of . We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger
than n
c
(where c is a large enough constant). Our main results are as follows:
Research supported by Israel Science Foundation (ISF) grant. 相似文献
1. | (For arbitrary k): For any n,k and any of size larger than n 20, we give an explicit construction for a function D : → , such that for any (n,k)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. |
2. | (For k=1): For any n and any of size larger than n c , we give an explicit construction for a function D: , such that for any (n, 1)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. Here, δ>0 is an arbitrary small constant, and c is a constant depending on δ. |
13.
We prove that an n-gon is pedal strong Fagnano trajectory in some convex polygonal billiard table if and only if it is a convex Poncelet n-gon.
相似文献
14.
In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞. 相似文献
15.
The purpose of this paper is to discuss a first-return integration process which yields the Lebesgue integral of a bounded
measurable function f: I → R defined on a compact interval I. The process itself, which has a Riemann flavor, uses the given function f and a sequence of partitions whose norms tend to 0. The “first-return” of a given sequence is used to tag the intervals from the partitions. The main result of the paper is that under rather general circumstances
this first return integration process yields the Lebesgue integral of the given function f for almost every sequence .
This research was initiated while the authors were in residence at the Mathematical Institute of St. Andrews University. 相似文献
16.
E. Ekici 《Acta Mathematica Hungarica》2007,117(4):325-333
The main purpose of this paper is to introduce the concepts of *-sets, *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of *-sets and some properties of -sets are discussed.
相似文献
17.
ChengJun Hou 《中国科学A辑(英文版)》2008,51(11):2089-2096
Let (F
ℚ) ×
α
ℤ be the crossed product von Neumann algebra of the free group factor (F
ℚ), associated with the left regular representation λ of the free group F
ℚ with the set {u
r
: r ∈ ℚ} of generators, by an automorphism α defined by α(λ(u
r
)) = exp(2πri)λ(u
r
), where ℚ is the rational number set. We show that (F
ℚ) ×
α
ℤ is a wΓ factor, and for each r ∈ ℚ, the von Neumann subalgebra generated in (F
ℚ) ×
α
ℚ by λ(u
r
) and υ is maximal injective, where υ is the unitary implementing the automorphism α. In particular, (F
ℚ) ×
α
℣ is a wΓ factor with a maximal abelian selfadjoint subalgebra which cannot be contained in any hyperfinite type II1 subfactor of (F
ℚ) ×
α
ℚ. This gives a counterexample of Kadison’s problem in the case of wΓ factor.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10201007, A0324614) and the Natural
Science Foundation of Shandong Province (Grant No. Y2006A03) 相似文献
18.
Let be a finite field with q elements, where q is a prime power. Let G be a subgroup of the general linear group over and be the rational function field over . We seek to understand the structure of the rational invariant subfield . In this paper, we prove that is rational (or, purely transcendental) by giving an explicit set of generators when G is the symplectic group. In particular, the set of generators we gave satisfies the Dickson property.
相似文献
19.
Hermano Frid 《Bulletin of the Brazilian Mathematical Society》2008,39(3):315-340
Let be a separable Hilbert space, an open convex subset, and f: a smooth map. Let Ω be an open convex set in with , where denotes the closure of Ω in . We consider the following questions. First, in case f is Lipschitz, find sufficient conditions such that for ɛ > 0 sufficiently small, depending only on Lip(f), the image of Ω by I + ɛf, (I + ɛf)(Ω), is convex. Second, suppose df(u): is symmetrizable with σ(df(u)) ⊆ (0,∞), for all u ∈ , where σ(df(u)) denotes the spectrum of df(u). Find sufficient conditions so that the image f(Ω) is convex. We establish results addressing both questions illustrating our assumptions and results with simple examples.
We also show how our first main result immediately apply to provide an invariance principle for finite difference schemes
for nonlinear ordinary differential equations in Hilbert spaces. The main application of the theory developed in this paper
concerns our second result and provides an invariance principle for certain convex sets in an L
2-space under the flow of a class of kinetic transport equations so called BGK model.
相似文献
20.
Let G be the complex general linear group and its Lie algebra equipped with a factorizable Lie bialgebra structure; let Uħ() be the corresponding quantum group. We construct explicit Uħ()-equivariant quantization of Poisson orbit bundles O
λ → O
μ in *. 相似文献