共查询到20条相似文献,搜索用时 31 毫秒
1.
Small into-isomorphism from L∞(A,μ) into L∞(B,υ) 总被引:1,自引:0,他引:1
DING Guanggui 《中国科学A辑(英文版)》2001,44(3):273-279
In this paper we shall assert that if T is an isomorphism of L∞(Ω1, A, μ) into L∞(Ω2, B, υ) satisfying the condition ‖T‖·‖T
−1‖⩽1+ɛ for ɛ∈
, then
is close to an isometry with an error less than 6ε in some conditions. 相似文献
2.
Letr, s ∈ [0, 1], and letX be a Banach space satisfying theM(r, s)-inequality, that is,
where π
X
is the canonical projection fromX
*** ontoX
*. We show some examples of Banach spaces not containingc
0, having the point of continuity property and satisfying the above inequality forr not necessarily equal to one. On the other hand, we prove that a Banach spaceX satisfying the above inequality fors=1 admits an equivalent locally uniformly rotund norm whose dual norm is also locally uniformly rotund. If, in addition,X satisfies
wheneveru
*,v
* ∈X
* with ‖u
*‖≤‖v
*‖ and (x
α
*
) is a bounded weak* null net inX
*, thenX can be renormed to satisfy the,M(r, 1) and theM(1, s)-inequality such thatX
* has the weak* asymptotic-norming property I with respect toB
X
. 相似文献
3.
Let (X, Xn; n ≥1) be a sequence of i.i.d, random variables taking values in a real separable Hilbert space (H, ||·||) with covariance operator ∑. Set Sn = X1 + X2 + ... + Xn, n≥ 1. We prove that, for b 〉 -1,
lim ε→0 ε^2(b+1) ∞ ∑n=1 (logn)^b/n^3/2 E{||Sn||-σε√nlogn}=σ^-2(b+1)/(2b+3)(b+1) B||Y|^2b+3
holds if EX=0,and E||X||^2(log||x||)^3bv(b+4)〈∞ where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator ∑, and σ^2 denotes the largest eigenvalue of ∑. 相似文献
lim ε→0 ε^2(b+1) ∞ ∑n=1 (logn)^b/n^3/2 E{||Sn||-σε√nlogn}=σ^-2(b+1)/(2b+3)(b+1) B||Y|^2b+3
holds if EX=0,and E||X||^2(log||x||)^3bv(b+4)〈∞ where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator ∑, and σ^2 denotes the largest eigenvalue of ∑. 相似文献
4.
A mapT: X→X on a normed linear space is callednonexpansive if ‖Tx-Ty‖≤‖x-y‖∀x, y∈X. Let (Ω, Σ,P) be a probability space,
an increasing chain of σ-fields spanning Σ,X a Banach space, andT: X→X. A sequence (xn) of strongly
-measurable and stronglyP-integrable functions on Ω taking on values inX is called aT-martingale if
.
LetT: H→H be a nonexpansive mapping on a Hilbert spaceH and let (xn) be aT-martingale taking on values inH. If
then x
n
/n converges a.e.
LetT: X→X be a nonexpansive mapping on ap-uniformly smooth Banach spaceX, 1<p≤2, and let (xn) be aT-martingale (taking on values inX). If
then there exists a continuous linear functionalf∈X
* of norm 1 such that
If, in addition, the spaceX is strictly convex, x
n
/n converges weakly; and if the norm ofX
* is Fréchet differentiable (away from zero), x
n
/n converges strongly.
This work was supported by National Science Foundation Grant MCS-82-02093 相似文献
5.
K. M. D'yakonov 《Journal of Mathematical Sciences》1996,78(2):131-141
Let ϕ be a unimodular function on the unit circle
and let Kp(ϕ) denote the kernel of the Toeplitz operator Tϕ in the Hardy space Hp, p≥1;
. Suppose Kp(ϕ)≠{0}. The problem is to find out how the smoothness of the symbol ϕ influences the boundary smoothness of functions in
Kp(ϕ). One of the main results is as follows.
Theorem 1 Let 1<p, q<+∞, 1<r≤+∞, q−1=p−1+r−1. Suppose |ϕ|≡1 on
and ϕ∈W
r
1
(i.e.,
). Then Kp(ϕ)⊂W
q
1
. Moreover, for any f∈Kp(ϕ) we have ‖f′‖q≤c(p, r)‖ϕ′‖r ‖f‖. Bibliography: 19 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 5–21.
Translated by K. M. D'yakonov. 相似文献
6.
Rajendra Bhatia 《印度理论与应用数学杂志》2010,41(1):99-111
Lipschitz continuity of the matrix absolute value |A| = (A*A)1/2 is studied. Let A and B be invertible, and let M
1 = max(‖A‖, ‖B‖), M
2 = max(‖A
−1‖, ‖B
−1‖). Then it is shown that
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
$
\left\| { \left| A \right| - \left| B \right| } \right\| \leqslant \left( {1 + log M_1 M_2 } \right) \left\| {A - B} \right\|
相似文献
7.
Let T(t), t ≥ 0, be a C
0-semigroup of linear operators acting in a Hilbert space H with norm ‖·‖. We prove that T(t) is uniformly bounded, i.e., ‖T(t)‖ ≤ M, t ≥ 0, if and only if the following condition is satisfied:
8.
J. Sunklodas 《Lithuanian Mathematical Journal》2007,47(3):327-335
We estimate the difference
for bounded functions h: ℝ → ℝ satisfying the Lipschitz condition, where Z
v
= B
v
−1
∑
i=0
∞
v
i
X
i
and
with discount factor ν such that 0 < ν < 1. Here {X
n
, n ≥ 0} is a sequence of strongly mixing random variables with
, and N is a standard normal random variable. In a particular case, the obtained upper bounds are of order O((1 − ν)1/2).
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 399–409, July–September, 2007.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-15/07. 相似文献
9.
Reinhard Wolf 《Israel Journal of Mathematics》1999,110(1):125-151
The average distance theorem of Gross implies that for each realN-dimensional Banach space (N≥2) there is a unique positive real numberr(E) with the following property: For each positive integern and for all (not necessarily distinct)x
1,x
2, …,x
n inE with ‖x
1‖=‖x
2‖=…=‖x
n‖=1, there exists anx inE with ‖x‖=1 such that
The main result of this paper shows, thatr(E)≤2−1/N for each realN-dimensional Banach spaceE (N≥2) with the so-called quasihypermetric property (which is equivalent toE isL
1-embeddable). Moreover, equality holds if and only ifE is isometrically isomorphic to ℝ
N
equipped with the usual 1-norm. 相似文献
10.
Claus Bauer 《数学学报(英文版)》1998,14(2):223-234
LetE(X)=‖{N≤X;N≠p
1
2
+p
2
3
+p
3
4
+p
4
5
for any primesp
i}‖. It is proved in this paper that there exists a positive constant δ>0 such that
11.
Kh. Kh. Ruzimuradov 《Journal of Mathematical Sciences》1996,79(5):1320-1324
Let Λ be a unimodular lattice in ℝ2, μ a homogeneous minimum of Λ; let P(a,b)⊂ℝ2 be a rectangle with vertices at the points (a,0), ...(0,b), P(a, b)+X its image under the translation by a vector X ∈ ℝ2. We prove that there exists a sequence of positive numbers v1<v2<...<vk<... with
, such that for u>μ the rectangle P(u, vk)+X contains T=S(P)+R points of Λ, where |R|<5; here S(P) is the area of the rectangle. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 82–89.
Translated by O. A. Ivanov. 相似文献
12.
V. K. Kharchenko 《Algebra and Logic》1997,36(2):133-144
Let L be a finite-dimensional restricted differential Lie C-algebra of R-continuous derivations of a prime ring R of characteristic
p>0, with generalized centroid C. We prove that if the associative inner part of L is quasi-Frobenius then R contains a nonzero
element a and elements v1,…,vn, such that for any x∈R we have the expansion
, where
are homorphisms of right RL-modules
. This gives rise to a certain relation on a ring over some subring, known as Shirshov local finiteness. The structure of
(R, RL)-subbimodules in a left Martindale ring of quotients is elucidated.
Supported by RFFR grant No. 95-01-01356a, and by the CONACYT of Mexico, Catedra Patrimonial 940411.
Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 219–238, March–April, 1997. 相似文献
13.
Krzysztof Cieplinski 《Czechoslovak Mathematical Journal》2005,55(4):1079-1088
Let
be a disjoint iteration group on the unit circle
, that is a family of homeomorphisms such that F
v1 ○ F
v2 = F
v1+v2 for v
1, v
2 ∈ V and each F
v
either is the identity mapping or has no fixed point ((V, +) is a 2-divisible nontrivial Abelian group). Denote by
the set of all cluster points of {F
v
(z), v ∈ V} for
. In this paper we give a general construction of disjoint iteration groups for which
. 相似文献
14.
The asymptotic expansions are studied for the vorticity
to 2D incompressible Euler equations with-initial vorticity
, where ϕ0(x) satisfies |d ϕ0(x)|≠0 on the support of
and
is sufficiently smooth and with compact support in ℝ2 (resp. ℝ2×T) The limit,v(t,x), of the corresponding velocity fields {v
ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω0(x). Moreover,
(ℤ2)) for all 1≽p∞, where
and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively. 相似文献
15.
The review article of Crandall, Ishii, and Lions [Bull. AMS,27, No. 1, 1–67 (1992)] devoted to viscosity solutions of first- and second-order partial differential equations contains the
exact Lax formula
16.
Mikhail Lifshits et Michel Weber 《Journal d'Analyse Mathématique》2003,89(1):1-14
We develop a spectral regularization technique for moving averages
, where ϕ is a nondecreasing map andU: H→H is a contraction of a Hilbert space (H, ‖·‖). We obtain a spectral regularization inequality which allows one to evaluate efficiently the increments ‖B
m
U
, ϕ (f)−B
n
U
, ϕ (f)‖,f∈H, by means of
where
is a properly regularized version of the spectral measure off with respect toU. We apply this inequality to an investigation of metric properties of the sets of moving averages {B
n
U, ϕ
(f), n ∈N} with fixedf∈H andN⊂ N. In particular, we obtain estimates of the associated covering numbers as well as of the related Littlewood-Paley-type
square functions. This work extends our previous results concerning the case of classical averages (ϕ(n)=0). Since it is well-known that the structure of general moving averages is more complicated, there is no surprise that
the general results we obtain are sometimes less complete than their classical counterparts and need suitable moment assumptions
on the spectral measure (depending on the growth of the shift function ϕ). Nevertheless, when applied to the classical situation,
our estimates still yield optimal bounds.
Avec pour le premier author, le soutien de la fondation russe pour la recherche fondamentale, subvention 99-01-00112 et INTAS subvention 99-01317. 相似文献 17.
Let {A, B} and {C, D} be diagonalizable pairs of order n, i.e., there exist invertible matrices P, Q and X, Ysuchthat A = P∧Q, B = PΩQ, C =XГY, D= X△Y, where
∧ = diag(α1, α2, …, αn), Ω= diag(βl, β2, …βn), Г=diag(γ1,γ2,…,γn), △=diag(δl,δ2,…,δn). Let ρ((α,β), (γ,δ))=|αδ-βγ|/√|α|^2+|β|^2√|γ|^2+|δ|^2.In this paper, it will be proved that there is a permutation τ of {1,2,... ,n} such that n∑i=1[ρ((αi,βi),(γτ(i),δτ(i)))]^2≤n[1-1/κ^2(Y)κ^2(Q)(1-d2F(Z,W)/n)], where κ(Y) = ||Y||2||Y^-1||2,Z= (A,B),W= (C, D) and dF(Z,W) = 1/√2||Pz* -Pw*||F. 相似文献 18.
WU Hao & LI Weigu School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,48(12):1670-1682
In this paper, we consider the following autonomous system of differential equations: x = Ax f(x,θ), θ = ω, where θ∈Rm, ω = (ω1,…,ωm) ∈ Rm, x ∈ Rn, A ∈ Rn×n is a constant matrix and is hyperbolic, f is a C∞ function in both variables and 2π-periodic in each component of the vector e which satisfies f = O(||x||2) as x → 0. We study the normal form of this system and prove that under some proper conditions this system can be transformed to an autonomous system: x = Ax g(x), θ = ω. Additionally, the proof of this paper naturally implies the extension of Chen's theory in the quasi-periodic case. 相似文献
19.
T. Sanders 《Journal d'Analyse Mathématique》2007,101(1):123-162
The paper has two main parts. To begin with, suppose that G is a compact abelian group. Chang’s Theorem can be viewed as a structural refinement of Bessel’s inequality for functions
ƒ ∈ L
2(G). We prove an analogous result for functions ƒ ∈ A(G), where A(G) is the space
endowed with the norm
, and generalize this to the approximate Fourier transform on Bohr sets.
As an application of the first part of the paper, we improve a recent result of Green and Konyagin. Suppose that p is a prime number and A ⊂ ℤ/pℤ has density bounded away from 0 and 1 by an absolute constant. Green and Konyagin have shown that ‖χ
A
‖
A(ℤ/pℤ) ≫ ɛ (log p)1/3−ɛ; we improve this to ‖χ
A
‖
A(ℤ/pℤ) ≫ ɛ (log p)1/2−ɛ. To put this in context, it is easy to see that if A is an arithmetic progression, then ‖χ
A
‖
A(ℤ/pℤ) ≪ log p. 相似文献
20.
Charles Li 《Israel Journal of Mathematics》2009,169(1):341-373
We prove that for a fixed non-archimedean place v of a totally real number field F, the traces of the associated Langlands classes of holomorphic cuspidal representations of GL2(A) with trivial central character and of prime levels is equidistributed with respect to the measure
|