共查询到20条相似文献,搜索用时 0 毫秒
1.
本文证明了(l^βn)的单位球面间的非满等距在一定条件下可被线性等距延拓至全空间。并刻画了l^p(P〉0)上的非满渐进可乘等距算子. 相似文献
2.
We study the problem of completely describing the domains that enjoy the generalized multiplicative inequalities of the embedding theorem type. We transfer the assertions for the Sobolev spaces L
p
1() to the function classes that result from the replacement of L
p
() with an ideal space of vector-functions. We prove equivalence of the functional and geometric inequalities between the norms of indicators and the capacities of closed subsets of . The most comprehensible results relate to the case of the rearrangement invariant ideal spaces. 相似文献
3.
Lipschitz Homogeneous Banach Spaces 总被引:1,自引:0,他引:1
4.
Vladimir V. Kisil 《Acta Appl Math》1999,59(1):79-109
We describe a construction of wavelets (coherent states) in Banach spaces generated by admissible group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example, we consider operator-valued Segal–Bargmann-type spaces and the Weyl functional calculus. 相似文献
5.
Very Convex Banach Spaces 总被引:7,自引:0,他引:7
VeryConvexBanachSpacesTegusi(特古斯)Suyalatu(苏雅拉图)(DepartmentofMathematics,InnerMongoliaNormalUniversity,Huhhot,010022)LiYongjin... 相似文献
6.
We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider some relations between K-very smoothness and other geometrical notions. 相似文献
7.
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
8.
The ideal space Id(A) of a Banach algebra A is studied as abitopological space Id(A), u, n, where u is the weakest topologyfor which all the norm functions I || a + I|| (with a A andI Id(A)) are upper semi-continuous, and n is the de Groot dualof u. When A is separable, nu is either a compact, metrizabletopology, or it is neither Hausdorff nor first countable. TAF-algebrasare shown to exhibit the first type of behaviour. Applicationsto Banach bundles (which motivate the study), and to PI-Banachalgebras, are given. 1991 Mathematics Subject Classification:46H10, 46J20. 相似文献
9.
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
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设E为一个Banach空间,(A,?,μ)是一个σ-有限的完全测度空间,本文引入了Bochner-Musielak-Orlicz空间L~?(A,E),得到了此空间的完备性.当E的对偶空间E~*具有Radon-Nikodym性质时,给出了L~?(A,E)的对偶空间.最后讨论这些空间的一致凸性和一致光滑性并给出它们的应用. 相似文献
14.
Journal of Theoretical Probability - We consider decoupling inequalities for random variables taking values in a Banach space X. We restrict the class of distributions that appear as conditional... 相似文献
15.
We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally
Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between
these polynomials and the corresponding linear operators.
(Received 17 May 1999; in revised form 6 October 1999) 相似文献
16.
Let X be a separable Banach space with dual X
*. A countable family of elements {g
i
}X
* is a p-frame (1 p ) if the norm
X
is equivalent to the
p
-norm of the sequence {g
i
()}. Without further assumptions, we prove that a p-frame allows every gX
* to be represented as an unconditionally convergent series g=d
i
g
i
for coefficients {d
i
}
q
, where 1/p+1/q=1. A p-frame {g
i
} is not necessarily linear independent, so {g
i
} is some kind of overcomplete basis for X
*. We prove that a q-Riesz basis for X
* is a p-frame for X and that the associated coefficient functionals {f
i
} constitutes a p-Riesz basis allowing us to expand every fX (respectively gX
*) as f=g
i
(f)f
i
(respectively g=g(f
i
)g
i
). In the general case of a p-frame such expansions are only possible under extra assumptions. 相似文献
17.
《Journal of Approximation Theory》2002,114(1):57-69
We prove that every Banach space containing a complemented copy of c0 has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space X, the set of all (equivalent) norms on X having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal norms in Banach spaces with the convex point of continuity property (CPCP). Other questions related to the existence of antiproximinal bodies are also discussed. 相似文献
18.
通过引入本性严格奇异算子和投影严格奇异算子,讨论本性不可比的Banach空间,对M.Gonzalez提出的猜想作出部分的肯定回答,最后,利用空间的本性不可比构造了一类空间,其上的非本性算子类和严格余奇异算子类是不重合的。 相似文献
19.
Let K be an ultrametric complete field and let E be an ultrametric space. Let A be the Banach K-algebra of bounded continuous functions from E to K and let B be the Banach K-algebra of bounded uniformly continuous functions from E to K. Maximal ideals and continuous multiplicative semi-norms on A (resp. on B) are studied by defining relations of stickiness and contiguousness on ultrafilters that are equivalence relations. So, the maximal spectrum of A (resp. of B) is in bijection with the set of equivalence classes with respect to stickiness (resp. to contiguousness). Every prime ideal of A or B is included in a unique maximal ideal and every prime closed ideal of A (resp. of B) is a maximal ideal, hence every continuous multiplicative semi-norms on A (resp. on B) has a kernel that is a maximal ideal. If K is locally compact, every maximal ideal of A (resp. of B) is of codimension 1. Every maximal ideal of A or B is the kernel of a unique continuous multiplicative semi-norm and every continuous multiplicative semi-norm is defined as the limit along an ultrafilter on E. Consequently, on A as on B the set of continuous multiplicative semi-norms defined by points of E is dense in the whole set of all continuous multiplicative semi-norms. Ultrafilters show bijections between the set of continuous multiplicative semi-norms of A, Max(A) and the Banaschewski compactification of E which is homeomorphic to the topological space of continuous multiplicative semi-norms. The Shilov boundary of A (resp. B) is equal to the whole set of continuous multiplicative semi-norms. 相似文献
20.
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