共查询到20条相似文献,搜索用时 62 毫秒
1.
Yu Can ZHU 《数学学报(英文版)》2007,23(9):1707-1718
In this paper, we introduce the concepts of q-Besselian frame and (p, σ)-near Riesz basis in a Banach space, where a is a finite subset of positive integers and 1/p+1/q = 1 with p 〉 1, q 〉 1, and determine the relations among q-frame, p-Riesz basis, q-Besselian frame and (p, σ)-near Riesz basis in a Banach space. We also give some sufficient and necessary conditions on a q-Besselian frame for a Banach space. In particular, we prove reconstruction formulas for Banach spaces X and X^* that if {xn}n=1^∞ C X is a q-Besselian frame for X, then there exists a p-Besselian frame {y&*}n=1^∞ belong to X^* for X^* such that x = ∑n=1^∞ yn^*(x)xn for all x ∈ X, and x^* =∑n=1^∞ x^*(xn)yn^* for all x^* ∈ X^*. Lastly, we consider the stability of a q-Besselian frame for the Banach space X under perturbation. Some results of J. R. Holub, P. G. Casazza, O. Christensen and others in Hilbert spaces are extended to Banach spaces. 相似文献
2.
Huai-Xin Cao Lan Li Qing-Jiang Chen Guo-Xing Ji 《Journal of Mathematical Analysis and Applications》2008,347(2):583-591
In this paper, (p,Y)-Bessel operator sequences, operator frames and (p,Y)-Riesz bases for a Banach space X are introduced and discussed as generalizations of the usual concepts for a Hilbert space and of the g-frames. It is proved that the set of all (p,Y)-Bessel operator sequences for a Banach space X is a Banach space and isometrically isomorphic to the operator space B(X,ℓp(Y)). Some necessary and sufficient conditions for a sequence of operators to be a (p,Y)-Bessel operator sequence are given. Also, a characterization of an independent (p,Y)-operator frame for X is obtained. Lastly, it is shown that an independent (p,Y)-operator frame for X is just a (p,Y)-Riesz basis for X and has a unique dual (q,Y*)-operator frame for X*. 相似文献
3.
In this paper we study Banach spaces that admit weighted Chebyshev centres for finite sets. Such spaces have been extensively studied recently by Veselý using the approach of finitely intersecting balls. Following his approach we exhibit large classes of Banach spaces that have this property. Certain stability results for spaces of vector valued continuous and Bochner integrable functions are also obtained. 相似文献
4.
R. Norvaisa 《Lithuanian Mathematical Journal》2005,45(4):447-457
We give a characterization of Gaussian chaos laws on Banach function spaces which do not contain ℓ
∞
n
's uniformly. The result is applied to describe the convergence in law of U-processes with sample paths in certain Banach function spaces.
__________
Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 553–566, October–December, 2005. 相似文献
5.
In this paper, we first show that for every mapping $f$ from a metric space $Ω$ to itself which is continuous off a countable subset of $Ω,$ there exists a nonempty
closed separable subspace $S ⊂ Ω$ so that $f|_S$ is again a self mapping on $S.$ Therefore,
both the fixed point property and the weak fixed point property of a nonempty closed
convex set in a Banach space are separably determined. We then prove that every
separable subspace of $c_0(\Gamma)$ (for any set $\Gamma$) is again lying in $c_0.$ Making use of these
results, we finally presents a simple proof of the famous result: Every non-expansive
self-mapping defined on a nonempty weakly compact convex set of $c_0(\Gamma)$ has a fixed
point. 相似文献
6.
Banach空间单位球面的球覆盖性质 总被引:5,自引:2,他引:3
证明了n维Banach空间的单位球面最少可被2n个不含原点的半径相同的球对称覆盖,并计算了空间(Rn,‖·‖2)中,单位球面可被∪in=1B(±rxi,r)(其中r∈R ,xi∈SX)覆盖时,r的最小值是2n,且球心{xi}ni=1构成了Rn的一组正交基. 相似文献
7.
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
8.
Ralf Kemper 《Applied Categorical Structures》2000,8(4):579-593
We show that the results about the set S : ={ [0, 1] 1 / p
x + (1 – )1 / p
z 1 / p
y + (1 – )1 / p
z}, where x, y, z elements of a p-absolutely convex space D and `' is a congruence relation on D are the best possible. Finally, we give an explicit construction of the left adjoint of the comparison functor Ô
p
: B an
p
T C
p
(resp. Ô
p, fin : V ec
p
A C
p
). 相似文献
9.
Tarn Adams 《Journal of Geometric Analysis》2008,18(1):1-28
We extend the notion of a flat chain with coefficients in a normed abelian group from Euclidean space to an arbitrary Banach
space and prove a compactness result. We also remove the condition that a flat chain with arbitrary coefficients have finite
mass in order for its support to exist.
This research was part of the author’s Ph. D. dissertation at Stanford University. 相似文献
10.
设E是带严格凸对偶空间的实可分Banach空间,设A:D(A)包含于E→E是一K正定算子。对任意f∈E,我们构造了强收敛于算子方程Ax=f唯一解的新的带误差的迭代过程。我们的工作推广了文[1,3-4]中的结果。 相似文献
11.
In this paper we study to what extent some classical results concerning operators T, from a
-space to a Banach space, or from a Banach space to a L
1-space, can be precised, when the Banach spaces involved are ordered (by a normal cone in the first case, by a closed generating
proper convex cone in the second case) and when the operators T are positive. 相似文献
12.
A necessary and sufficient condition for an operator in a Banach ideal space to be a prediction operator is given. 相似文献
13.
André Adler Andrew Rosalsky Andrej I. Volodin 《Journal of Theoretical Probability》1997,10(3):605-623
For a sequence of constants {a
n,n1}, an array of rowwise independent and stochastically dominated random elements { V
nj, j1, n1} in a real separable Rademacher type p (1p2) Banach space, and a sequence of positive integer-valued random variables {T
n, n1}, a general weak law of large numbers of the form
is established where {c
nj, j1, n1},
n , b
n are suitable sequences. Some related results are also presented. No assumption is made concerning the existence of expected values or absolute moments of the {V
nj, j1, n1}. Illustrative examples include one wherein the strong law of large numbers fails. 相似文献
14.
Banach空间的K—M逼近 总被引:1,自引:0,他引:1
设X是自反、严格凸且具有H性质的Banach空间,A是X的弱序列完备子集。本文证明了A是可逼近紧的Chebyshev集的充分必要条件是A是太阳集;同时,也讨论了Orlicz序列空间的太阳集。 相似文献
15.
16.
Niels Jakob Laustsen 《K-Theory》2001,23(2):115-127
We prove that the K-groups of the Banach algebra
of bounded, linear operators on the pth James space
, where 1 < p < , are given by
and
. Moreover, for each Banach space
and each non-zero, closed ideal
contained in the ideal of inessential operators, we show that
and
. This enables us to calculate the K-groups of
for each Banach space
which is a direct sum of finitely many James spaces and
-spaces. 相似文献
17.
Henryk Hudzik Yuwen Wang Ruli Sha 《Numerical Functional Analysis & Optimization》2013,34(7-8):779-790
In this paper, we extend the Moreau (Riesz) decomposition theorem from Hilbert spaces to Banach spaces. Criteria for a closed subspace to be (strongly) orthogonally complemented in a Banach space are given. We prove that every closed subspace of a Banach space X with dim X ≥ 3 (dim X ≤ 2) is strongly orthognally complemented if and only if the Banach space X is isometric to a Hilbert space (resp. strictly convex), which is complementary to the well-known result saying that every closed subspace of a Banach space X is topologically complemented if and only if the Banach space X is isomorphic to a Hilbert space. 相似文献
18.
讨论Banach空间几种超投影性质(及其相应的局部化性质)之间的关系,证明了在Banach空间X自反的条件下,X是lp-次投影空间的充要条件是X*是lp-超投影空间,X是局部lp-次投影空间的充要条件是X*是局部lp-超投影空间,以及X是局部次投影空间的充要条件是X*是局部超投影的。其中1/p+1/q=1(p>1,q>1)。 相似文献
19.
On Hereditarily Indecomposable Banach Spaces 总被引:1,自引:0,他引:1
Li Xin CHENG Huai Jie ZHONG 《数学学报(英文版)》2006,22(3):751-756
This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm. 相似文献
20.
We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. 相似文献