共查询到20条相似文献,搜索用时 31 毫秒
1.
We study when a Banach space with absolute norm may have polynomial numerical indices equal to one. In the real case, we show that a Banach space X with absolute norm, which has the Radon-Nikodým property or is Asplund, satisfies n(2)(X)<1 unless it is one-dimensional. In the complex case, we show that the only Banach spaces X with absolute norm and the Radon-Nikodým property which satisfy n(2)(X)=1 are the spaces . Also, the only Asplund complex space X with absolute norm which satisfies n(2)(X)=1 is c0(Λ). 相似文献
2.
S. Dhompongsa T. Domínguez Benavides A. Kaewcharoen A. Kaewkhao B. Panyanak 《Journal of Mathematical Analysis and Applications》2006,320(2):916-927
The purpose of this paper is to study the existence of fixed points for nonexpansive multivalued mappings in a particular class of Banach spaces. Furthermore, we demonstrate a relationship between the weakly convergent sequence coefficient WCS(X) and the Jordan–von Neumann constant CNJ(X) of a Banach space X. Using this fact, we prove that if CNJ(X) is less than an appropriate positive number, then every multivalued nonexpansive mapping has a fixed point where E is a nonempty weakly compact convex subset of a Banach space X, and KC(E) is the class of all nonempty compact convex subsets of E. 相似文献
3.
Theω′-topology on the spaceL(X, Y) of bounded linear operators from the Banach spaceX into the Banach spaceY is discussed in [10]. Let ℒw' (X, Y) denote the space of allT∈L(X, Y) for which there exists a sequence of compact linear operators (T
n)⊂K(X, Y) such thatT=ω′−limnTn and let
. We show that
is a Banach ideal of operators and that the continuous dual spaceK(X, Y)* is complemented in
. This results in necessary and sufficient conditions forK(X, Y) to be reflexive, whereby the spacesX andY need not satisfy the approximation property. Similar results follow whenX andY are locally convex spaces.
Financial support from the Potchefstroom University and Maseno University is greatly acknowledged.
Financial support from the NRF and Potchefstroom University is greatly acknowledged. 相似文献
4.
R. Choukri A. El Kinani A. Oukhouya 《Rendiconti del Circolo Matematico di Palermo》2007,56(2):235-243
We characterize locally convex topological algebrasA satisfying: a sequence (x
n) inA converges to 0 if, and only if, (x
n
2) converges to 0. We also show that a real Banach algebra such thatx
n
2+y
n
2→0 if, and only if,x
n → 0 andy
n → 0, for every sequences (x
n) and (y
n) inA, is isomorphic to, whereX is a compact space.
相似文献
5.
The aim of this paper is to study Birkhoff integrability for multi-valued maps , where (Ω,Σ,μ) is a complete finite measure space, X is a Banach space and cwk(X) is the family of all non-empty convex weakly compact subsets of X. It is shown that the Birkhoff integral of F can be computed as the limit for the Hausdorff distance in cwk(X) of a net of Riemann sums ∑nμ(An)F(tn). We link Birkhoff integrability with Debreu integrability, a notion introduced to replace sums associated to correspondences when studying certain models in Mathematical Economics. We show that each Debreu integrable multi-valued function is Birkhoff integrable and that each Birkhoff integrable multi-valued function is Pettis integrable. The three previous notions coincide for finite dimensional Banach spaces and they are different even for bounded multi-valued functions when X is infinite dimensional and X∗ is assumed to be separable. We show that when F takes values in the family of all non-empty convex norm compact sets of a separable Banach space X, then F is Pettis integrable if, and only if, F is Birkhoff integrable; in particular, these Pettis integrable F's can be seen as single-valued Pettis integrable functions with values in some other adequate Banach space. Incidentally, to handle some of the constructions needed we prove that if X is an Asplund Banach space, then cwk(X) is separable for the Hausdorff distance if, and only if, X is finite dimensional. 相似文献
6.
We present a robust representation theorem for monetary convex risk measures
r: X ? \mathbbR{\rho : \mathcal{X} \rightarrow \mathbb{R}} such that
limnr(Xn) = r(X) whenever (Xn) almost surely converges to X,\lim_n\rho(X_n) = \rho(X)\,{\rm whenever}\,(X_n)\,{\rm almost\,surely\,converges\,to}\,X, 相似文献
7.
For Ω bounded and open subset of
andX a reflexive Banach space with 1-symmetric basis, the function spaceJF
X
(Ω) is defined. This class of spaces includes the classical James function space. Every member of this class is separable
and has non-separable dual. We provide a proof of topological nature thatJF
X
(Ω) does not contain an isomorphic copy of ℓ1. We also investigate the structure of these spaces and their duals. 相似文献
8.
The multiplicative spectrum of a complex Banach space X is the class
(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X, *) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with unity. Properties of multiplicative spectra are studied. In particular,
we show that
(X
n
) consists of countable compact spaces with at most n nonisolated points for any separable, hereditarily indecomposable Banach space X. We prove that
(C[0, 1]) coincides with the class of all metrizable compact spaces.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 14, Algebra,
2004. 相似文献
9.
A. A. Fora 《Periodica Mathematica Hungarica》1985,16(2):97-113
In this paper, we definen-segmentwise metric spaces and then we prove the following results:
10.
Viorel Vâjâitu 《Czechoslovak Mathematical Journal》2016,66(2):493-509
We consider a convexity notion for complex spaces X with respect to a holomorphic line bundle L over X. This definition has been introduced by Grauert and, when L is analytically trivial, we recover the standard holomorphic convexity. In this circle of ideas, we prove the counterpart of the classical Remmert’s reduction result for holomorphically convex spaces. In the same vein, we show that if H0(X,L) separates each point of X, then X can be realized as a Riemann domain over the complex projective space Pn, where n is the complex dimension of X and L is the pull-back of O(1). 相似文献
11.
Let X and Y be Banach spaces. A set
(the space of all weakly compact operators from X into Y) is weakly equicompact if, for every bounded sequence (x
n) in X, there exists a subsequence (x
k(n)) so that (Txk(n)) is uniformly weakly convergent for T ∈ M. In this paper, the notion of weakly equicompact set is used to obtain characterizations of spaces X such that
X ↩̸ ℓ1, of spaces X such that B
X*
is weak* sequentially compact and also to obtain several results concerning to the weak operator and the strong operator
topologies. As another application of weak equicompactness, we conclude a characterization of relatively compact sets in
when this space is endowed with the topology of uniform convergence on the class of all weakly null sequences. Finally, we
show that similar arguments can be applied to the study of uniformly completely continuous sets.
Received: 5 July 2006 相似文献
12.
13.
Rafael Dahmen 《Mathematische Zeitschrift》2010,266(1):115-140
We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: The group DiffGerm (K, X) of germs of analytic diffeomorphisms around a compact set K in a Banach space X and the group ${\bigcup_{n\in\mathbb {N}}G_n}
14.
T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1997,107(1):35-42
In this paper we study a geometric property for Banach spaces called condition (*), introduced by de Reynaet al in [3], A Banach space has this property if for any weakly null sequencex
n of unit vectors inX, ifx
*
n
is any sequence of unit vectors inX
* that attain their norm at xn’s, then
. We show that a Banach space satisfies condition (*) for all equivalent norms iff the space has the Schur property. We also
study two related geometric conditions, one of which is useful in calculating the essential norm of an operator. 相似文献
15.
Let X and Y be Banach spaces. We say that a set
(the space of all weakly compact operators from X into Y) is weakly equicompact if, for every bounded sequence (xn) in X, there exists a subsequence (xk(n)) so that (Txk(n)) is weakly uniformly convergent for T ∈ M. We study some properties of weakly equicompact sets and, among other results, we prove: 1) if
is collectively weakly compact, then M* is weakly equicompact iff M** x**={T** x** : T ∈ M} is relatively compact in Y for every x** ∈X**; 2) weakly equicompact sets are precompact in
for the topology of uniform convergence on the weakly null sequences in X.
Received: 14 February 2005; revised: 1 June 2005 相似文献
16.
P. van der Cruyssen 《BIT Numerical Mathematics》1982,22(4):533-537
Consider the (n+1)st order nonhomogeneous recursionX
k+n+1=b
k
X
k+n
+a
k
(n)
X
k+n-1+...+a
k
(1)
X
k
+X
k
.Leth be a particular solution, andf
(1),...,f
(n),g independent solutions of the associated homogeneous equation. It is supposed thatg dominatesf
(1),...,f
(n) andh. If we want to calculate a solutiony which is dominated byg, but dominatesf
(1),...,f
(n), then forward and backward recursion are numerically unstable. A stable algorithm is derived if we use results constituting a link between Generalised Continued Fractions and Recursion Relations. 相似文献
17.
Paulette Saab 《Aequationes Mathematicae》1980,20(1):252-262
LetX be any compact convex subset of a locally convex Hausdorff space andE be a complex Banach space. We denote byA(X, E) the space of all continuous and affineE-valued functions defined onX. In this paper we prove thatX is a Choquet simplex if and only if the dual ofA(X, E) is isometrically isomorphic by a selection map toM
m
(X, E*), the space ofE*-valued,w*-regular boundary measures onX. This extends and strengthens a result of G. M. Ustinov. To do this we show that for any compact convex setX, each element of the dual ofA(X, E) can be represented by a measure inM
m
(X, E*) with the same norm, and this representation is unique if and only ifX is a Choquet simplex. We also prove that ifX is metrizable andE is separable then there exists a selection map from the unit ball of the dual ofA(X, E) into the unit ball ofM
m
(X, E*) which is weak* to weak*-Borel measurable.This work will constitute a portion of the author's Ph.D. Thesis at the University of Illinois. 相似文献
18.
G. Schlüchtermann 《manuscripta mathematica》1991,73(1):397-409
A sufficient condition is given when a subspaceL⊂L
1(μ,X) of the space of Bochner integrable function, defined on a finite and positive measure space (S, Φ, μ) with values in a Banach spaceX, is locally uniformly convex renormable in terms of the integrable evaluations {∫
A
fdμ;f∈L}. This shows the lifting property thatL
1(μ,X) is renormable if and only ifX is, and indicates a large class of renormable subspaces even ifX does not admit and equivalent locally uniformly convex norm. 相似文献
19.
We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. LetS n(F) be the space of alln×n symmetry matrices over a fieldF with 2,3 ∈F *, thenT is an additive injective operator preserving rank-additivity onS n(F) if and only if there exists an invertible matrixU∈M n(F) and an injective field homomorphism ? ofF to itself such thatT(X)=cUX ?UT, ?X=(xij)∈Sn(F) wherec∈F *,X ?=(?(x ij)). As applications, we determine the additive operators preserving minus-order onS n(F) over the fieldF. 相似文献
20.
In this paper we study the spaces ∞p(E, X) of p-lattice summing operators from a Banach space E to a Banach lattice X. The main results characterize those E and X for which Δp(E, X) = IIp(E, X) and we show that ∞(E, X)=Δ2(E, X) for an infinite dimensional Banach lattice X of finite cotype if and only if E is isomorphic to a Hilbert space. 相似文献
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