共查询到20条相似文献,搜索用时 234 毫秒
1.
L. Weis 《Mathematische Nachrichten》1984,119(1):321-326
For every bounded linear operator T in L1[0, 1] there is an element of best approximation in the ideal of weakly compact operators. We also give some sufficient conditions for ‖T+S‖ = ‖T‖ + ‖S‖, where S and T are L1-operators. 相似文献
2.
Let q be a prime power, ??q be the field of q elements, and k, m be positive integers. A bipartite graph G = Gq(k, m) is defined as follows. The vertex set of G is a union of two copies P and L of two‐dimensional vector spaces over ??q, with two vertices (p1, p2) ∈ P and [ l1, l2] ∈ L being adjacent if and only if p2 + l2 = pl. We prove that graphs Gq(k, m) and Gq′(k′, m′) are isomorphic if and only if q = q′ and {gcd (k, q ? 1), gcd (m, q ? 1)} = {gcd (k′, q ? 1),gcd (m′, q ? 1)} as multisets. The proof is based on counting the number of complete bipartite INFgraphs in the graphs. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 322–328, 2005 相似文献
3.
In Sook Park 《Mathematische Nachrichten》2008,281(4):561-574
It is shown that for any locally compact abelian group ?? and 1 ≤ p ≤ 2, the Fourier type p norm with respect to ?? of a bounded linear operator T between Banach spaces, denoted by ‖T |?????p‖, satisfies ‖T |?????p‖ ≤ ‖T |?????p‖, where ?? is the direct product of ?2, ?3, ?4, … It is also shown that if ?? is not of bounded order then Cnp ‖T |?????p‖ ≤ ‖T |?????p‖, where ?? is the circle group, n is a onnegative integer and Cp = . From these inequalities, for any locally compact abelian group ?? ‖T |?????2‖ ≤ ‖T |?????2‖, and moreover if ?? is not of bounded order then ‖T |?????2‖ = ‖T |?????2‖. The Hilbertian property and B‐convexity are discussed in the framework of Fourier type p norms. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
In this paper, with the help of spectral integral, we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces. Precisely, let H be a complex Hilbert space and 0 ε 1/2. Then for every bounded linear operator T : H → H and x0 ∈ H with ||T|| = 1 = ||x0|| such that ||Tx0|| 1 ε, there exist xε∈ H and a bounded linear operator S : H → H with||S|| = 1 = ||xε|| such that ||Sxε|| = 1, ||xε-x0|| ≤ (2ε)1/2 + 4(2ε)1/2, ||S-T|| ≤(2ε)1/2. 相似文献
5.
Minkyun Kim C.J. Neugebauer 《Journal of Mathematical Analysis and Applications》2002,275(2):575-585
We introduce a bound M of f, ‖f‖∞?M?2‖f‖∞, which allows us to give for 0?p<∞ sharp upper bounds, and for −∞<p<0 sharp lower bounds for the average of |f|p over E if the average of f over E is zero. As an application we give a new proof of Grüss's inequality estimating the covariance of two random variables. We also give a new estimate for the error term in the trapezoidal rule. 相似文献
6.
Tetiana V. Ivashyna 《Central European Journal of Mathematics》2013,11(9):1677-1688
Let X and Y be Banach spaces. An operator G: X → Y is a Daugavet center if ‖G +T‖ = ‖G‖+‖T‖ for every rank-1 operator T. For every Daugavet center G we consider a certain set of operators acting from X, so-called G-narrow operators. We prove that if J is the natural embedding of Y into a Banach space E, then E can be equivalently renormed so that an operator T is (J ○ G)-narrow if and only if T is G-narrow. We study G-rich subspaces of X: Z ? X is called G-rich if the quotient map q: X → X/Z is G-narrow. 相似文献
7.
Justin Holmer 《偏微分方程通讯》2013,38(5):878-905
We consider solutions u(t) to the 3d NLS equation i? t u + Δu + |u|2 u = 0 such that ‖xu(t)‖ L 2 = ∞ and u(t) is nonradial. Denoting by M[u] and E[u], the mass and energy, respectively, of a solution u, and by Q(x) the ground state solution to ?Q + ΔQ + |Q|2 Q = 0, we prove the following: if M[u]E[u] < M[Q]E[Q] and ‖u 0‖ L 2 ‖?u 0‖ L 2 > ‖Q‖ L 2 ‖?Q‖ L 2 , then either u(t) blows-up in finite positive time or u(t) exists globally for all positive time and there exists a sequence of times t n → + ∞ such that ‖?u(t n )‖ L 2 → ∞. Similar statements hold for negative time. 相似文献
8.
《随机分析与应用》2013,31(6):1177-1189
New very general univariate and multivariate probabilistic Ostrowski type inequalities are established, involving ‖·‖∞ and ‖·‖ p , p≥1 norms of probability density functions. Some of these inequalities provide pointwise estimates to the error of probability distribution function from the expectation of some simple function of the engaged random variable. Other inequalities give upper bounds for the expectation and variance of a random variable. All are done over finite domains. At the end are given applications, especially for the Beta random variable. 相似文献
9.
Jipu Ma 《Frontiers of Mathematics in China》2014,9(5):1089-1103
Let E be a Banach space with the cl-norm||·|| in E/{0}, and let S(E) = {e ∈ E: ||e|| = 1}. In this paper, a geometry characteristic for E is presented by using a geometrical construct of S(E). That is, the following theorem holds: the norm of E is of eI in E/{0} if and only if S(E) is a c1 submanifold of E, with codimS(E) = 1. The theorem is very clear, however, its proof is non-trivial, which shows an intrinsic connection between the continuous differentiability of the norm ||·|| in E/{0} and differential structure of S(E). 相似文献
10.
Suppose G=(V, E) is a graph and p ≥ 2q are positive integers. A (p, q)‐coloring of G is a mapping ?: V → {0, 1, …, p‐1} such that for any edge xy of G, q ≤ |?(x)‐?(y)| ≤ p‐q. A color‐list is a mapping L: V → ({0, 1, …, p‐1}) which assigns to each vertex v a set L(v) of permissible colors. An L‐(p, q)‐coloring of G is a (p, q)‐coloring ? of G such that for each vertex v, ?(v) ∈ L(v). We say G is L‐(p, q)‐colorable if there exists an L‐(p, q)‐coloring of G. A color‐size‐list is a mapping ? which assigns to each vertex v a non‐negative integer ?(v). We say G is ?‐(p, q)‐colorable if for every color‐list L with |L(v)| = ?(v), G is L‐(p, q)‐colorable. In this article, we consider list circular coloring of trees and cycles. For any tree T and for any p ≥ 2q, we present a necessary and sufficient condition for T to be ?‐(p, q)‐colorable. For each cycle C and for each positive integer k, we present a condition on ? which is sufficient for C to be ?‐(2k+1, k)‐colorable, and the condition is sharp. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 249–265, 2007 相似文献
11.
Let H : Lp ( R ) → Lp( R ), 1 < p < ∞ be the real HILBERT transform. A bounded, linear operator u:E → F (E, F BANACH spaces) is a HT-operator, if the mapping u ? H : E ? L2( R , E) → L2( R , F) has a bounded, linear extension to L2( R ) → L2( R , F). For E = F and u = idE BOURGAIN [3] and BURKHOLDER [5] have shown that this holds if and only if E ? UMD. We study these HT-operators and, in particular, we construct a HT-operator which is not UMD-factorable. Furthermore, we show that a UMD-space E is a HILBERT space if and only if |idE ? H| = 1. 相似文献
12.
O. I. Reinov 《Journal of Mathematical Sciences》2000,102(5):4487-4507
The following question concerning the computation of the norms of the tensor products of operators in the Lebesgue spaces is studied: Is it true that the norm of the tensor product A?B: Lp(μ?μ)→Lq(ν?ν) of operators A: Lp(μ)→Lq(ν) and B: Lp(μ)→Lq(ν) coincides with the product ‖A‖ ‖B‖ of their norms? An answer is positive if and only if 1≤p≤q≤+∞. Bibliography: 26 titles. 相似文献
13.
ABSTRACT The variational problem in L ∞ considered is to minimize F(u) = ‖Du‖ L ∞(Ω) subject to ∈ t Ω |Du|2 dx ≤ E for given E > 0. It is proven that a constrained minimizer exists and satisfies an Aronsson-Euler equation in the viscosity sense which depends on a parameter Λ∞ ≥ 0. This parameter splits Ω into two parts. In one part the minimizer satisfies the infinity laplace equation and in the remaining part the minimizer is the solution of the elasto-plastic torsion problem with constraint ‖Du‖ L ∞ ≤ Λ∞. 相似文献
14.
Let ‖·‖ be a norm on the algebra ?n of all n × n matrices over ?. An interesting problem in matrix theory is that “Are there two norms ‖·‖1 and ‖·‖2 on ?n such that ‖A‖ = max|‖Ax‖2: ‖x‖1 = 1} for all A ∈ ?n?” We will investigate this problem and its various aspects and will discuss some conditions under which ‖·‖1 = ‖·‖2. 相似文献
15.
For 0<p<+∞ let hp be the harmonic Hardy space and let bp be the harmonic Bergman space of harmonic functions on the open unit disk U. Given 1?p<+∞, denote by ‖⋅bp‖ and ‖⋅hp‖ the norms in the spaces bp and hp, respectively. In this paper, we establish the harmonic hp-analogue of the known isoperimetric type inequality ‖fb2p‖?‖fhp‖, where f is an arbitrary holomorphic function in the classical Hardy space Hp. We prove that for arbitrary p>1, every function f∈hp satisfies the inequality
‖fb2p‖?ap‖fhp‖, 相似文献
16.
Luis A. Caffarelli 《偏微分方程通讯》2013,38(3):391-414
Consider a function u defined on n , except, perhaps, on a closed set of potential singularities . Suppose that u solves the eikonal equation ‖Du‖ = 1 in the pointwise sense on n \, where Du denotes the gradient of u and ‖·‖ is a norm on n with the dual norm ‖·‖?. For a class of norms which includes the standard p-norms on n , 1 < p < ∞, we show that if has Hausdorff 1-measure zero and n ≥ 2, then u is either affine or a “cone function,” that is, a function of the form u(x) = a ± ‖x ? z‖?. 相似文献
17.
Richard A Alò André de Korvin Vo Van Tho 《Journal of Mathematical Analysis and Applications》1978,63(3):563-590
For a Banach space E and for 1 ? p < ∞ let ?p<∞ let LEp(μ) = LEp(S,B,μ) denote all Bochner p-integrable E-valued functions on a measure space (S,B,μ). Under study are convergence theorems for integrals of functions in LEp(μ) with respect to Nemytskii measures. Weak integrals are then denoted to Hammerstein operators, and a study of topologies generated by vector measures leads to a characterization of compact Hammerstein operators. 相似文献
18.
Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition supx ≠0(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
Let M be a Cartan-Hadamard manifold of dimension d ≧ 3, let p ? M and x = exp {r(x)θ(x)} be geodesic polar coordinates with pole p and let X be the Brownian motion on M. Let SectM(x) denote the sectional curvature of any plane section in Mx. We prove that for each c > 2, there is a 0 < β < 1 such that if - L2r(x)2β ≦ SectM(x) ≦ -cr(x)?2 for all x in the complement of a compact set, then limt → ∞ θ(Xt) exists a.s. and defines a nontrivial invariant random variable. The Dirichlet problem at infinity and a conjecture of Greene and Wu are also discussed. 相似文献
20.
Isabelle Chalendar 《Journal of Functional Analysis》2009,256(4):1258-1268
An operator between Banach spaces is said to be finitely strictly singular if for every ε>0 there exists n such that every subspace E⊆X with dimE?n contains a vector x such that ‖Tx‖<ε‖x‖. We show that, for 1?p<q<∞, the formal inclusion operator from Jp to Jq is finitely strictly singular. As a consequence, we obtain that the strictly singular operator with no invariant subspaces constructed by C. Read is actually finitely strictly singular. These results are deduced from the following fact: if k?n then every k-dimensional subspace of Rn contains a vector x with ‖x?∞‖=1 such that xmi=i(−1) for some m1<?<mk. 相似文献