共查询到20条相似文献,搜索用时 31 毫秒
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.
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
3.
We discuss the relations among the best approximation E
n
(f) and the Fourier coefficients of a function, under the conditions that and , where MVBVS* is the class of the so-called Strong Mean Value Bounded Variation Sequences.
This work was supported by NSERC RCD grant and AARMS of Canada (Yu D S), by NSERC of Canada (Zhou P), and by the National
Natural Science Foundation of China (Grant No. 10471130) and the Open Fund (Grant No. PLN0613) of State Key Laboratory of
Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (Zhou S P) 相似文献
4.
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
5.
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
6.
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
7.
Let G be an additive subgroup of a normed space X. We say that a point is weakly separated (resp. -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions:
(ws) if , then x is weakly separated from G;
(ps) if , then x is -separated from G;
(wp) if Tx is -separated from T(G), then x is weakly separated from G.
By (resp. , ) we denote the class of operators T : X → Y which satisfy (ws) (resp. (ps), (wp)) for all and all subgroups G of X. The paper is an attempt to describe the above classes of operators for various Banach spaces X, Y. It is proved that if X, Y are Hilbert spaces, then is the class of Hilbert-Schmidt operators. It is also shown that if T is a Hilbert-to-Banach space operator with finite ℓ-norm, then .
相似文献
8.
Let 0 → I → A → A/I → 0 be a short exact sequence of C*-algebras with A unital. Suppose that the extension 0 → I → A → A/I → 0 is quasidiagonal, then it is shown that any positive element (projection, partial isometry, unitary element, respectively)
in A/I has a lifting with the same form which commutes with some quasicentral approximate unit of I consisting of projections. Furthermore, it is shown that for any given positive number ε, two positive elements (projections,
partial isometries, unitary elements, respectively) in A/I, and a positive element (projection, partial isometry, unitary element, respectively) a which is a lifting of , there is a positive element (projection, partial isometry, unitary element, respectively) b in A which is a lifting of such that ∥a−b∥ < . As an application, it is shown that for any positive numbers ε and in U(A/I)
0
, there exists u in U(A)0 which is a lifting of such that cel(u) < cel.
This work was supported by National Natural Science Foundation of China (Grant No. 10771161) 相似文献
9.
G. Androulakis P. Dodos G. Sirotkin V. G. Troitsky 《Israel Journal of Mathematics》2009,169(1):221-250
V. D. Milman proved in [20] that the product of two strictly singular operators on L
p
[0, 1] (1 ⩽ p < 1) or on C[0, 1] is compact. In this note we utilize Schreier families in order to define the class of -strictly singular operators, and then we refine the technique of Milman to show that certain products of operators from this
class are compact, under the assumption that the underlying Banach space has finitely many equivalence classes of Schreier-spreading
sequences. Finally we define the class of -hereditarily indecomposable Banach spaces and we examine the operators on them.
This project originated at SUMIRFAS conference in 2005 in Texas A&M University. The authors wish to thank the organizers of
the SUMIRFAS conference for their hospitality. 相似文献
10.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively. 相似文献
11.
Projectively condensed semigroups,generalized completely regular semigroups and projective orthomonoids 总被引:1,自引:0,他引:1
The class of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety
of . Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of . We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain
the structure theorems of various generalized orthogroups.
Partially supported by a UGC (HK) grant #2060123 (04-05). 相似文献
12.
Yonutz V. Stanchescu 《Combinatorica》2008,28(3):343-355
We describe the structure of three dimensional sets of lattice points, having a small doubling property. Let be a finite subset of ℤ3 such that dim = 3. If and , then lies on three parallel lines. Moreover, for every three dimensional finite set that lies on three parallel lines, if , then is contained in three arithmetic progressions with the same common difference, having together no more than terms. These best possible results confirm a recent conjecture of Freiman and cannot be sharpened by reducing the quantity
υ or by increasing the upper bounds for . 相似文献
13.
Michel Weber 《Results in Mathematics》2007,51(1-2):141-179
Let where are independent Bernoulli random variables. In relation with the divisor problem, we evaluate the almost sure asymptotic
order of the sums , where and is a sequence of positive integers.
Received: May 23, 2007. Revised: June 8, 2007. 相似文献
14.
Alessandra Cherubini 《Milan Journal of Mathematics》2007,75(1):305-321
A word w over a finite alphabet Σ is called k-collapsing if for each finite deterministic automaton the inequality holds provided that for some word , depending on . A word over the alphabet Σ is called k-synchronizing if it is a reset word for all synchronizing automata with k + 1 states and input alphabet Σ. The aim of this work is to give the motivations of the interest in these words and to provide
an overview of some results in this area.
Received: May 2007 相似文献
15.
Changguo Wei 《Proceedings Mathematical Sciences》2008,118(4):517-524
Some results on A
-algebras are given. We study the problem when ideals, quotients and hereditary subalgebras of A
-algebras are A
-algebras or A
-algebras, and give a necessary and sufficient condition of a hereditary subalgebra of an A
-algebra being an A
-algebra. 相似文献
16.
Stephan Ramon Garcia 《Integral Equations and Operator Theory》2008,60(3):357-367
If denotes the polar decomposition of a bounded linear operator T, then the Aluthge transform of T is defined to be the operator . In this note we study the relationship between the Aluthge transform and the class of complex symmetric operators (T iscomplex symmetric if there exists a conjugate-linear, isometric involution so that T = CT*C). In this note we prove that: (1) the Aluthge transform of a complex symmetric operator is complex symmetric, (2) if T is complex symmetric, then and are unitarily equivalent, (3) if T is complex symmetric, then if and only if T is normal, (4) if and only if T
2 = 0, and (5) every operator which satisfies T
2 = 0 is necessarily complex symmetric.
This work partially supported by National Science Foundation Grant DMS 0638789. 相似文献
17.
Furstenberg family and chaos 总被引:3,自引:0,他引:3
Jin-cheng XlONG~ Jie L Feng TAN School of Mathematical Sciences South China Normal University Guangzhou China 《中国科学A辑(英文版)》2007,50(9):1325-1333
A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A■B and A∈F imply B∈F.For a given system (i.e.,a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family F, the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family F.In the present paper we explore the basic properties of the set of F-scrambled pairs of a system.The generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed. 相似文献
18.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2008,151(2):2907-2923
New solutions of twist equations for the universal enveloping algebras U (An−1) are found. These solutions can be represented as products of full chains of extended Jordanian twists Abelian factors (“rotations”) , and sets of quasi-Jordanian twists . The latter are generalizations of Jordanian twists (with carrier b2) for special deformed extensions of the Hopf algebra U (b2). The carrier subalgebra for the composition is a nonminimal parabolic subalgebra in A
n−1 such that . The parabolic twisting elements are obtained in an explicit form. Details of the construction are illustrated by considering the examples n = 4 and n = 11.
Bibliography: 21 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 187–213. 相似文献
19.
A family of transitive modular Lie superalgebras with depth one 总被引:1,自引:0,他引:1
Wen-de LIU~ 《中国科学A辑(英文版)》2007,50(10):1451-1466
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=(?)satisfying the conditions: (i)g0(?)(g-1)and g0-module g-1 is isomorphic to the natural(?)(g-1)-module; (ii)dim g1=2/3n(2n~2 1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered. 相似文献
20.
Concettina Galati 《Rendiconti del Circolo Matematico di Palermo》2009,58(2):211-243
Let be a smooth family of surfaces whose general fibre is a smooth surface of ℙ3 and whose special fibre has two smooth components, intersecting transversally along a smooth curve R. We consider the Universal Severi-Enriques variety on . The general fibre of is the variety of curves on in the linear system with k cusps and δ nodes as singularities. Our problem is to find all irreducible components of the special fibre of . In this paper, we consider only the cases (k, δ) = (0, 1) and (k, δ) = (1, 0). In particular, we determine all singular curves on the special fibre of which, counted with the right multiplicity, are a limit of 1-cuspidal curves on the general fibre of .
相似文献