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1.
We prove that for cardinalsτ satisfying τω=τ and forτ=ω
1, there do not exist universal Eberlein Compacts of weightτ, or universal WCG spaces of density characterτ. Ifτ is a strong limit cardinal of countable cofinality such universal spaces do exist. Thus under GCH universal spaces exist
forτ iff cof(τ)=ω.
The research of the second author was supported by a grant from the United States-Israel Binational Science Foundation and
the Fund for the Promotion of Research at the Technion. 相似文献
2.
Daryl Tingley 《Applicable analysis》2013,92(1-3):1-4
D. P. Mil'man and V. D. Mil'man considered sequences of decreasing nonempty closed bounded convex sets with empty intersection to obtain characteristics of non-reflexivity. They showed that in every nonreflexive space there is such a sequence which is ω-separated. We show that in every nonreflexive space there is also always such a sequence which is not ω-separated 相似文献
3.
Nina M. Roy 《Israel Journal of Mathematics》1974,17(2):142-148
Square Banach spaces are characterized among real Banach spaces in terms of the Alfsen-Effros structure topology on the extreme
points of the dual ball. As a corollary, one has that the class of separable square spaces coincides with the class of separableG-spaces. It is also shown that for aG-space (hence for a square space) regularity of the quotient structure topology is equivalent to complete regularity, and
that square spaces exist for which this topology is not regular.
Part of this paper is from the author’s Ph.D. thesis prepared at Bryn Mawr College under the direction of Professor Frederic
Cunningham, Jr., whose valuable guidance is greatly appreciated by the author. 相似文献
4.
On strongly WCG Banach spaces 总被引:2,自引:0,他引:2
5.
Jesús Bastero 《Israel Journal of Mathematics》1986,53(3):373-380
In this paper we prove the following result which solves a question raised by A. Pelczynski: “Every stable Banach space with
an unconditional basis is isomorphic to a complemented subspace of some stable Banach space with a symmetric basis.” Moreover,
we show that all the interpolation spacesl
p
,l
q
θ,X,1 1≦p, q<∞ andX stable, are stable. 相似文献
6.
Spiros A. Argyros Sophocles Mercourakis 《Proceedings of the American Mathematical Society》2005,133(3):773-785
We present two examples of WCG spaces that are not hereditarily WCG. The first is a space with an unconditional basis, and the second is a space such that is WCG and does not contain . The non-WCG subspace of has the additional property that is not WCG and is reflexive.
7.
David P. McLaughlin 《Mathematische Zeitschrift》1992,211(1):189-194
This paper is based on part of the author's Ph.D. thesis written under the supervision of Professor V. Zizler and has been
supported in part by a Province of Alberta Graduate Fellowship 相似文献
8.
Normal structure of banach spaces 总被引:1,自引:0,他引:1
W. L. Bynum 《manuscripta mathematica》1974,11(3):203-209
GOSSEZ and LAMI DOZO have obtained a sufficient condition for a Banach space with a Schauder basis to have normal structure. This paper generalizes their theorem to obtain a sufficient condition for an arbitrary Banach space to have normal structure. An example is given to show an application of the theorem.Research supported by a Faculty Research Grant of the College of William and Mary. 相似文献
9.
Gunnar Sparr 《Annali di Matematica Pura ed Applicata》1974,99(1):247-316
Summary Peetre's K- and J-methods for interpolation are extended to the situation of more than two spaces. The theory developed is
applied to interpolation of Lp-spaces with weights and to spaces of Besov and Sobolev type.
Entrata in Redazione il 5 luglio 1972. 相似文献
10.
T. Amahroq A. Jourani L. Thibault 《Numerical Functional Analysis & Optimization》2013,34(3-4):215-226
This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space. 相似文献
11.
12.
A structure theorem for Banach spaces whose duals areL
1 spaces, is proved.
The research of the second named author has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR
66-18 through the European Office of Aerospace Research (OAR) United States Air Force. 相似文献
13.
E. V. Oshman 《Mathematical Notes》1971,10(4):697-701
The paper provides the complete characteristics of the class of reflexive strictly convex spaces in which the metric projections on each convex closed set are continuous.Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 459–468, October, 1971.The author wishes to thank S. B. Stechkin for useful comments. 相似文献
14.
Manuel Valdivia 《manuscripta mathematica》1975,15(2):153-163
15.
For the Azimi-Hagler spaces more geometric and topological properties are investigated. Any constructed space is denoted by
X
α,p
. We show
相似文献
(i) | The subspace [(e nk )] generated by a subsequence (e nk ) of (e n ) is complemented. |
(ii) | The identity operator from X α,p to X α,p when p > q is unbounded. |
(iii) | Every bounded linear operator on some subspace of X α,p is compact. It is known that if any X α,p is a dual space, then |
(iv) | duals of X α,1 spaces contain isometric copies of ℓ ∞ and their preduals contain asymptotically isometric copies of c 0. |
(v) | We investigate the properties of the operators from X α,p spaces to their predual. |
16.
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
17.
It is proved using positive definite functions that a normed spaceX is unifomly homeomorphic to a subset of a Hilbert space, if and only ifX is (linearly) isomorphic to a subspace of aL
0(μ) space (=the space of the measurable functions on a probability space with convergence in probability). As a result we get
thatl
p
(respectivelyL
p
(0, 1)), 2<p<∞, is not uniformly embedded in a bounded subset of itself. This answers negatively the question whether every infinite dimensional
Banach space is uniformly homeomorphic to a bounded subset of itself. Positive definite functions are also used to characterize
geometrical properties of Banach spaces.
Partially supported by the National Science Foundation, Grant MCS-79-03322.
Partially supported by the National Science Foundation, Grant MCS-80-06073. 相似文献
18.
P. W. Meyer 《Numerical Functional Analysis & Optimization》2013,34(3-4):249-259
A Kantorowitsch-analysis of Newton's method in generalized Banach spaces is given. The application of generalized norms – mappings from a linear space into a partially ordered Banach space - improves convergence results and error estimatescompared with the real norm theory. 相似文献
19.
20.
Ferrante Balboni 《Annali di Matematica Pura ed Applicata》1998,175(1):339-364
We give a generalization, for smooth Fredholm maps between Banach spaces, of the Preparation Theorem known in finite dimension. As an application we obtain the Prepared Form Theorem which is a basic tool in singularity theory. 相似文献