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1.
The α-modulation spaces , α∈[0,1], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for α-modulation spaces in the multivariate setting. The frames constructed are unions of independent Riesz sequences based on tensor products of univariate brushlet functions, which simplifies the analysis of the full frame. We show that the multivariate α-modulation spaces can be completely characterized by the Banach frames constructed. 相似文献
2.
3.
4.
5.
We prove that every Banach space can be isometrically and 1-complementably embedded into a Banach space which satisfies property
β and has the same character of density. Then we show that, nevertheless, property β satisfies a hereditary property. We study
strong subdifferentiability of norms with property β to characterize separable polyhedral Banach spaces as those admitting
a strongly subdifferentiable β norm. In general, a Banach space with such a norm is polyhedral. Finally, we provide examples
of non-reflexive spaces whose usual norm fails property β and yet it can be approximated by norms with this property, namely
(L
1[0,1], ‖·‖1) and (C(K), ‖·‖∗) whereK is a separable Hausdorff compact space
To the memory of A. Plans
Supported in part by DGICYT grant PB 94-0243 and DGICYT PB 96-0607. 相似文献
6.
Having discussed the parameter in [5] we introduce in this paper a volume parameter We give some properties of it, and obtain that P_3(x)<4 if X is 2UR, and that X is a super-reflexive Banach space if p_3(x)<4. 相似文献
7.
Let λ>1. We prove that every separable Banach space E can be embedded isometrically into a separable ℒ
∞
λ
-spaceX such thatX/E has the RNP and the Schur property. This generalizes a result in [2]. Various choices ofE allow us to answer several questions raised in the literature. In particular, takingE = ℓ2, we obtain a ℒ
∞
λ
-spaceX with the RNP such that the projective tensor product
containsc
0 and hence fails the RNP. TakingE=L
1, we obtain a ℒ
∞
λ
-space failing the RNP but nevertheless not containingc
0. 相似文献
8.
Sokol Bush Kaliaj 《Monatshefte für Mathematik》2014,175(4):555-564
A Banach–Zarecki Theorem for a Banach space-valued function \(F : [0,1] \rightarrow X\) with compact range is presented. We define the strong absolute continuity ( \(sAC_{||.||_{F}}\) ) and the bounded variation ( \(BV_{||.||_{F}}\) ) of \(F\) with respect to the Minkowski functional \(||.||_{F}\) associated to the closed absolutely convex hull \(C_{F}\) of \(F([0,1])\) . It is proved that \(F\) is \(sAC_{||.||_{F}}\) if and only if \(F\) is \(BV_{||.||_{F}}\) , weak continuous on \([0,1]\) and satisfies the weak property \((N)\) . 相似文献
9.
In this paper, we compute the -, - and -duals of the sequence spaces , the -dual of the sequence spaces and the -dual of the sequence spaces and . 相似文献
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11.
12.
O. S. Gretskii 《Ukrainian Mathematical Journal》1994,46(10):1472-1479
We study the monogeneity conditions for -differentiable mappings of domains of a Banach space and establish criteria of -differentiability of a mapping at a point.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1336–1342, October, 1994. 相似文献
13.
Letx
1,x
2, ...,x
n
ben unit vectors in a normed spaceX and defineM
n
=Ave{‖Σ
i=1
n
ε1
x
i
‖:ε1=±1}. We prove that there exists a setA⊂{1, ...,n} of cardinality
such that {x
i
}
i∈A
is 16M
n
-isomorphic to the natural basis ofl
∞
k
. This result implies a significant improvement of the known results concerning embedding ofl
∞
k
in finite dimensional Banach spaces. We also prove that for every ∈>0 there exists a constantC(∈) such that every normed spaceX
n
of dimensionn either contains a (1+∈)-isomorphic copy ofl
2
m
for somem satisfying ln lnm≧1/2 ln lnn or contains a (1+∈)-isomorphic copy ofl
∞
k
for somek satisfying ln lnk>1/2 ln lnn−C(∈). These results follow from some combinatorial properties of vectors with ±1 entries.
The contribution of the first author to this paper forms part of his Ph.D. Thesis written under the supervision of Prof. M.
A. Perles from the Hebrew University. 相似文献
14.
Suppose that E and E′ denote real Banach spaces with dimension at least 2, that D $ \subseteq $ E and D′ $ \subseteq $ E′ are domains, that f: D → D′ is an (M,C)-CQH homeomorphism, and that D is uniform. The aim of this paper is to prove that D′ is a uniform domain if and only if f extends to a homeomorphism $\overline f :\overline D \to {\overline D ^\prime }$ and $\overline f $ is η-QM relative to ?D. This result shows that the answer to one of the open problems raised by Väisälä from 1991 is affirmative. 相似文献
15.
Aleksandr Yur’evich Ivanov 《Journal of Mathematical Sciences》2013,192(4):417-425
An analog of the well-known problem of partition of figures into parts with less diameter in Banach spaces is studied. The sufficient conditions for the sets to belong to the class of Borsuk’s sets in multidimensional Banach spaces are first obtained. 相似文献
16.
It is shown that a Banach spaceX admits an equivalent uniformly Gateaux smooth norm if and only if the dual ball ofX* in its weak star topology is a uniform Eberlein compact.
Supported by AV 101-97-02, AV 1019003 and GA ČR 201-98-1449.
Supported by GA ČR 201-98-1449, AV 1019003 and GAUK 1/1998. 相似文献
17.
Markus Seidel 《Journal of Functional Analysis》2012,262(11):4916-4927
In this paper we extend the concept of the -pseudospectra of Hansen to the case of bounded linear operators on Banach spaces and prove several relations to the usual spectrum. We particularly discuss the approximation by rectangular finite sections and the impact of the fundamental result of Shargorodsky on “jumping” pseudospectra. 相似文献
18.
. , , . . 相似文献
19.
On K_0-groups of operator algebras on Banach spaces 总被引:1,自引:0,他引:1
ZHANG Yunnan ZHONG Huaijie & SU Weigang School of Mathematics Computer Science Fujian Normal University Fuzhou China 《中国科学A辑(英文版)》2006,49(2)
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0. 相似文献
20.
In this paper, we introduce the weakly relaxed ??-pseudomonotone mapping which generalizes the class of pseudomonotone mappings. Some examples are given which show that the weakly relaxed ??-pseudomonotonicity is a proper generalization of pseudomonotonicity for both scalar and vector valued bi-functions. Using the KKM technique, we establish the existence of solutions of equilibrium problems and vector equilibrium problems with weakly relaxed ??-pseudomonotonicity in the reflexive Banach spaces. The present work extends some corresponding results of the variational-like inequalities (Fang and Huang in J. Optim. Theory Appl. 118:327?C338, 2003; Lee and Lee in J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 11: 231?C242, 2004) to equilibrium problems. 相似文献