共查询到20条相似文献,搜索用时 15 毫秒
1.
S. J. Dilworth E. Odell T. Schlumprecht A. Zsák 《Foundations of Computational Mathematics》2008,8(6):703-736
Let (e
i
) be a dictionary for a separable infinite-dimensional Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn
usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach
space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c
0. We also show that, for every ε>0, the unit ball of every separable infinite-dimensional Banach space X contains a dictionary (x
i
) such that the additive group generated by (x
i
) is (3+ε)−1-separated and 1/3-dense in X.
相似文献
2.
《复变函数与椭圆型方程》2012,57(10):827-835
The analytic map g on the unit disk D is said to induce a multiplication operator L from the Banach space X to the Banach space Y if L(f)=f·g∈Y for all f∈X. For z ∈ D and α>0 the families of weighted Cauchy transforms Fα are defined by ?(z) = ∫T Kx α (z)dμ(x) where μ(x) is complex Borel measures, x belongs to the unit circle T and the kernel Kx (z) = (1- xz)?1. In this article we will explore the relationship between the compactness of the multiplication operator L acting on F 1 and the complex Borel measures μ(x). We also give an estimate for the essential norm of L 相似文献
3.
Let {T(t)}t≥0 be a C0–semigroup on a Banach space X with generator A, and let H∞T be the space of all x ∈ X such that the local resolvent λ ↦ R(λ, A)x has a bounded holomorphic extension to the right half–plane. For the class of integrable functions ϕ on [0, ∞) whose Fourier transforms are integrable, we construct a functional calculus ϕ ↦ Tϕ, as operators on H∞T. Weshow that each orbit T(·)Tϕx is bounded and uniformly continuous, and T(t)Tϕx → 0 weakly as t → ∞, and we give a new proof that ∥T(t)R(μ, A)x∥ = O(t). We also show that ∥T(t)Tϕx∥ → 0 when T is sun –reflexive, and that ∥T(t)R(μ, A)x∥ = O(ln t) when T is a positive semigroup on a normal ordered space X and x is a positive vector in H∞T. 相似文献
4.
Let X be a Banach space with closed unit ball B. Given k
, X is said to be k-β, respectively, (k + 1)-nearly uniformly convex ((k + 1)-NUC), if for every ε > 0 there exists δ, 0 < δ < 1, so that for every x B and every ε-separated sequence (xn) B there are indices (ni)ki = 1, respectively, (ni)k + 1i = 1, such that (1/(k + 1))||x + ∑ki = 1 xni|| ≤ 1 − δ, respectively, (1/(k + 1))||∑k + 1i = 1 xni|| ≤ 1 − δ. It is shown that a Banach space constructed by Schachermayer is 2-β, but is not isomorphic to any 2-NUC Banach space. Modifying this example, we also show that there is a 2-NUC Banach space which cannot be equivalently renormed to be 1-β. 相似文献
5.
Stanislav Shkarin 《Mathematische Nachrichten》2003,257(1):87-98
Let X be a real Banach space, ω : [0, +∞) → ? be an increasing continuous function such that ω(0) = 0 and ω(t + s) ≤ ω(t) + ω(s) for all t, s ∈ [0, +∞). According to the infinite dimensional analog of the Osgood theorem if ∫10 (ω(t))?1 dt = ∞, then for any (t0, x0) ∈ ?×X and any continuous map f : ?×X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all t ∈ ?, x, y ∈ X, the Cauchy problem (t) = f(t, x(t)), x(t0) = x0 has a unique solution in a neighborhood of t0. We prove that if X has a complemented subspace with an unconditional Schauder basis and ∫10 (ω(t))?1 dt < ∞ then there exists a continuous map f : ? × X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all (t, x, y) ∈ ? × X × X and the Cauchy problem (t) = f(t, x(t)), x(t0) = x0 has no solutions in any interval of the real line. 相似文献
6.
Yehoram Gordon 《Israel Journal of Mathematics》1969,7(2):151-163
Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ
p(X) as inf{Σ
i
=1/m
|x*(x
i)|p
p Σ
i
=1/m
‖x
i‖p
p]1
p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x
1,x
2, …,x
m} ⊂X such that Σ
i
=1/m
‖x
i‖>0. It follows immediately from [2] thatμ
p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ
p(X) for various spaces, and obtain some asymptotic estimates ofμ
p(X) for general finite dimensional Banach spaces.
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
A. Dvoretzky and Prof. J. Lindenstrauss. 相似文献
7.
We show that the set of all inner derivations of an ultraprime real Banach algebra is closed within all bounded derivations. More concretely, we show that for such an algebra A there exists a positive number γ (depending only on the “constant of ultraprimeness” of A) satisfying γ ∥ a+Z(A) ∥≦∥ D a ∥ for all a in A, where Z(A) denotes the centre of A and D a denotes the inner derivation on A induced by a. This result is an extension of the corresponding complex version obtained by the authors in [Proc. Amer. Math. Soc., to appear]. The proof relies on the following theorem: ultraproducts of a family of central ultraprime real Banach algebras with a unit and with constant of ultraprimeness greater than or equal to a fixed positive constant K are central ultraprime Banach algebras with a unit. This fact is obained via a general result for real Banach algebras that reads as follows: If A is a central real Banach algebra with a unit 1, then for every a in A satisfying ∥ 1+a 2 ∥<1 we have [1+√1?||1+1a 2||]2≦2(|?l+M a ||+||D a ||) where M a denotes the two-sided multiplication operator by a on A. 相似文献
8.
Yossi Moshe 《Journal d'Analyse Mathématique》2006,99(1):267-294
Let λ be the upper Lyapunov exponent corresponding to a product of i.i.d. randomm×m matrices (X
i)
i
0/∞
over ℂ. Assume that theX
i's are chosen from a finite set {D
0,D
1...,D
t-1(ℂ), withP(X
i=Dj)>0, and that the monoid generated byD
0, D1,…, Dq−1 contains a matrix of rank 1. We obtain an explicit formula for λ as a sum of a convergent series. We also consider the case
where theX
i's are chosen according to a Markov process and thus generalize a result of Lima and Rahibe [22].
Our results on λ enable us to provide an approximation for the numberN
≠0(F(x)n,r) of nonzero coefficients inF(x)
n.(modr), whereF(x) ∈ ℤ[x] andr≥2. We prove the existence of and supply a formula for a constant α (<1) such thatN
≠0(F(x)n,r) ≈n
α for “almost” everyn.
Supported in part by FWF Project P16004-N05 相似文献
9.
J Désarménien 《Advances in Mathematics》1978,29(1):11-14
Let A be a Jordan algebra over the reals which is a Banach space with respect to a norm satisfying the requirements: (i) ∥ a ° b ∥ ≤ ∥ a ∥ ∥ b ∥, (ii) ∥ a2 ∥ = ∥ a ∥2, (iii) ∥ a2 ∥ ≤ ∥ a2 + b2 ∥ for a, b?A. It is shown that A possesses a unique norm closed Jordan ideal J such that has a faithful representation as a Jordan algebra of self-adjoint operators on a complex Hilbert space, while every “irreducible” representation of A not annihilating J is onto the exceptional Jordan algebra M38. 相似文献
10.
LetX be a closed subset of a topological spaceF; leta(·) be a continuous map fromX intoX; let {x
i} be a sequence generated iteratively bya(·) fromx
0 inX, i.e.,x
i+1 =a(x
i),i=0, 1, 2, ...; and letQ(x
0) be the cluster point set of {x
i}. In this paper, we prove that, if there exists a pointz inQ(x
0) such that (i)z is isolated with respect toQ(x
0), (ii)z is a periodic point ofa(·) of periodp, and (iii)z possesses a sequentially compact neighborhood, then (iv)Q(x
0) containsp points, (v) the sequence {x
i} is contained in a sequentially compact set, and (vi) every point inQ(x
0) possesses properties (i) and (ii). The application of the preceding results to the caseF=E
n leads to the following: (vii) ifQ(x
0) contains one and only one point, then {x
i} converges; (viii) ifQ(x
0) contains a finite number of points, then {x
i} is bounded; and (ix) ifQ(x
0) containsp points, then every point inQ(x
0) is a periodic point ofa(·) of periodp. 相似文献
11.
Let [A, a] be a normed operator ideal. We say that [A, a] is boundedly weak*-closed if the following property holds: for all Banach spaces X and Y, if T: X → Y** is an operator such that there exists a bounded net (T
i
)
i∈I
in A(X, Y) satisfying lim
i
〈y*, T
i
x
y*〉 for every x ∈ X and y* ∈ Y*, then T belongs to A(X, Y**). Our main result proves that, when [A, a] is a normed operator ideal with that property, A(X, Y) is complemented in its bidual if and only if there exists a continuous projection from Y** onto Y, regardless of the Banach space X. We also have proved that maximal normed operator ideals are boundedly weak*-closed but, in general, both concepts are different.
相似文献
12.
Let X be a real Banach space and let (f(n)) be a positive nondecreasing sequence. We consider systems of unit vectors (xi)∞i=1 in X which satisfy ∑iA±xi|A|−f(|A|), for all finite A
and for all choices of signs. We identify the spaces which contain such systems for bounded (f(n)) and for all unbounded (f(n)). For arbitrary unbounded (f(n)), we give examples of systems for which [xi] is H.I., and we exhibit systems in all isomorphs of ℓ1 which are not equivalent to the unit vector basis of ℓ1. We also prove that certain lacunary Haar systems in L1 are quasi-greedy basic sequences. 相似文献
13.
Markus Haase 《Integral Equations and Operator Theory》2006,56(2):197-228
We generalize a Hilbert space result by Auscher, McIntosh and Nahmod to arbitrary Banach spaces X and to not densely defined injective sectorial operators A. A convenient tool proves to be a certain universal extrapolation space associated with A. We characterize the real interpolation space
( X,D( Aa ) ?R( Aa ) )q,p{\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)} \cap \mathcal{R}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}}
as
{ x ? X|t - q\textRea y1 ( tA )x, t - q\textRea y2 ( tA )x ? L*p ( ( 0,¥ );X ) } {\left\{ {x\, \in \,X|t^{{ - \theta {\text{Re}}\alpha }} \psi _{1} {\left( {tA} \right)}x,\,t^{{ - \theta {\text{Re}}\alpha }} \psi _{2} {\left( {tA} \right)}x \in L_{*}^{p} {\left( {{\left( {0,\infty } \right)};X} \right)}} \right\}} 相似文献
14.
Jon Chaika 《Geometric And Functional Analysis》2011,21(5):1020-1042
Given an IET T : [0, 1) → [0, 1) and decreasing sequence of positive real numbers with divergent sum a = {ai}¥i=1{{\bf a} = \{a_i\}^\infty_{i=1}} we consider
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