共查询到20条相似文献,搜索用时 31 毫秒
1.
After some introductory propositions, we give a dual characterization of those locally convex spaces which satisfy the Mackey
convergence condition or the fast convergence condition by means of Schwartz topologies. Making use of the universal Schwartz
space (l
∞
,τ(l
∞
,l
1)) we prove some representation theorems for bornological and ultrabornological spaces, that is, every bornological spaceE is a dense subspace of an inductive limit lim indE
a, a∈A, ofseparable Banach spacesE
a, and every Mackey null sequence inE is a null sequence in someE
a. IfE is ultrabornological, thenE can be represented as lim indE
a,a∈A, allE
a separable Banach spaces, such that every fast null sequence inE is a null sequence in someE
a. 相似文献
2.
Defant [5] introduced the local Radon–Nikodym property for duals of locally convex spaces. This is a generalization of Asplund
spaces as defined in Banach space theory. In this paper we generalise Dunford"s Theorem [7] to Banach spaces with Schauder
decompositions and apply this result to spaces of holomorphic functions on balanced domains in a Banach space.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
Bengt Josefson 《Israel Journal of Mathematics》1990,71(3):321-327
An example of a Banach spaceE is given with the following properties: Every bounding setA⊂E (i.e.f(A) is bounded for each holomorphic functionf:E →C) is relatively compact but there are relatively non-compact limited setsA (i.e.T(A) is relatively compact for each bounded linear mapT:E →c
0). 相似文献
4.
Jorgen Vesterstrom 《Israel Journal of Mathematics》1973,16(2):203-211
The following result is proved: letE be anF-space (that is, the space of all continuous affine functions defined on a compact universal cap van shing at zero) and letMχE be anM-ideal. Then, ifE/M is a π1 with positive defining projections, then there is a positive linear operator ϱ:E/M→E of norm one such that ϱ lifts the canonical mapE→E/M. In the proof, which heavily depends on work of Ando, we study ensor products of certain convex cones with compact bases,
and we calculate the norm of a positive linear operator defined on a finite dimensional space with range in aF-space. Various corollaries are deduced for split faces of compact convex sets and for morphisms ofC
*-algebras. 相似文献
5.
Gilles Godefroy 《Israel Journal of Mathematics》1981,38(3):209-220
We study in this work various aspects of the isometric theory of duality. We show that in wide classes of Banach spaces, dual
spaces are characterized by the existence of a retraction fromE″ ontoE. The predual of such spaces is then unique. We study the imbedding of regularly normed spaces into dual spaces. We better
the known results on loss of regularity of the norm of dual spaces. We characterize the dual norms on an Asplund space in
terms of “bad differentiability”.
相似文献
6.
Coenraad C.A. Labuschagne 《Positivity》2006,10(2):391-407
Let E and F be Banach lattices and let S, T: E→ F be positive operators such that 0≤ S≤ T. It is shown that if T is a Radon–Nikodym operator, F has order continuous norm and E and F both have (Schaefer's) property (P), then S is a Radon–Nikodym operator; also, if T is an Asplund operator, E' has order continuous norm and E has property (P), then S is an Asplund operator. 相似文献
7.
A. Szankowski 《Israel Journal of Mathematics》1972,11(3):292-296
We construct a separable reflexive Banach spaceX which is complementably universal for all finite dimensional Banach spaces. By this we mean: for every finite dimensional
Banach spaceE there is isometric embeddingi:E→X such that there exists a projectionP: →
→
onto
with ‖P‖=1. 相似文献
8.
Christopher Boyd 《Monatshefte für Mathematik》2000,130(3):177-188
We develop a duality theory for spaces of approximable n-homogeneous polynomials on locally convex spaces, generalising results previously obtained for Banach spaces. For E a Fréchet space with its dual having the approximation property and with E′
b
locally Asplund we show that the space of n-homogeneous polynomials on (E′
b
)′
b
is the inductive dual of the space of boundedly weakly continuous n-homogeneous polynomials on E. We show that when E is a reflexive Fréchet space, the space of n-homogeneous polynomials on E is reflexive if and only if every n-homogeneous polynomial on E is boundedly weakly continuous.
(Received 24 March 1999; in final form 14 February 2000) 相似文献
9.
Christopher Boyd 《Monatshefte für Mathematik》2000,18(4):177-188
We develop a duality theory for spaces of approximable n-homogeneous polynomials on locally convex spaces, generalising results previously obtained for Banach spaces. For E a Fréchet space with its dual having the approximation property and with E′ b locally Asplund we show that the space of n-homogeneous polynomials on (E′ b )′ b is the inductive dual of the space of boundedly weakly continuous n-homogeneous polynomials on E. We show that when E is a reflexive Fréchet space, the space of n-homogeneous polynomials on E is reflexive if and only if every n-homogeneous polynomial on E is boundedly weakly continuous. 相似文献
10.
Philip J. Boland 《Arkiv f?r Matematik》1977,15(1):87-91
LetU be an open subset of a complex locally convex spaceE, andH(U) the space of holomorphic functions fromU toC. If the dualE′ ofE is nuclear with respect to the topology generated by the absolutely convex compact subsets ofE, then it is shown thatH(U) endowed with the compact open topology is a nuclear space. In particular, ifE is the strong dual of a Fréchet nuclear space, thenH(U) is a Fréchet nuclear space. 相似文献
11.
A closed, convex and bounded setP in a Banach spaceE is called a polytope if every finite-dimensional section ofP is a polytope. A Banach spaceE is called polyhedral ifE has an equivalent norm such that its unit ball is a polytope. We prove here:
We deduce from these two results that in a polyhedral Banach space (for instance in c0(ℕ) or inC(K) forK countable compact), every equivalent norm can be approximated by norms which are analytic onE/{0}. 相似文献
(1) | LetW be an arbitrary closed, convex and bounded body in a separable polyhedral Banach spaceE and let ε>0. Then there exists a tangential ε-approximating polytopeP for the bodyW. |
(2) | LetP be a polytope in a separable Banach spaceE. Then, for every ε>0,P can be ε-approximated by an analytic, closed, convex and bounded bodyV. |
12.
Let (E) be the space of complex valued holomorphic functions on a complex Banach space E. The approximation property for (E), endowed with various natural locally convex topologies, is studied. For example, (E) with the compact-open topology has the approximation property if and only if E has the approximation property. In order to characterize when (E) has the approximation property for topologies other than the compact-open, the notion of a compact holomorphic map between Banach spaces in introduced and studied. 相似文献
13.
Riesz product spaces and representation theory 总被引:1,自引:0,他引:1
Let {E
i:i∈I} be a family of Archimedean Riesz spaces. The Riesz product space is denoted by ∏
i∈I
Ei. The main result in this paper is the following conclusion: There exists a completely regular Hausdorff spaceX such that ∏
i∈I
Ei is Riesz isomorphic toC(X) if and only if for everyi∈I there exists a completely regular Hausdorff spaceX
i such thatE
i is Riesz isomorphic toC(X
i).
Supported by the National Natural Science Foundation of China 相似文献
14.
N. T. Peck 《Israel Journal of Mathematics》1993,81(3):357-368
LetF be a quasi-linear map on a separable normed spaceE, and assume thatF splits on an infinite-dimensional subspace ofE. Then the twisted sum topology on ℝ⊗F
E can be written as the supremum of a nearly convex topology and a trivial dual topology. (This partially answers a question
of Klee.) The result applies to the Ribe space and to James’s space.
To victor Klee 相似文献
15.
It is proved that ifE is a separable Banach lattice withE′ weakly sequentially complete,F is a Banach space andT:E→F is a bounded linear operator withT′F′ non-separable, then there is a subspaceG ofE, isomorphic toC(Δ), such thatT
G is an isomorphism, whereC(Δ) denotes the space of continuous real valued functions on the Cantor discontinuum. This generalizes an earlier result of
the second-named author. A number of conditions are proved equivalent for a Banach latticeE to contain a subspace order isomorphic toC(Δ). Among them are the following:L
1 is lattice isomorphic to a sublattice ofE′;C(Δ)′ is lattice isomorphic to a sublattice ofE′; E contains an order bounded sequence with no weak Cauchy subsequence;E has a separable closed sublatticeF such thatF′ does not have a weak order unit.
The research of both authors was partially supported by the National Science Foundation, NSF Grant No MPS 71-02839 A04. 相似文献
16.
Jean Saint Raymond 《Rendiconti del Circolo Matematico di Palermo》1995,44(1):162-168
Let (T, ℐ, μ) be a σ-finite atomless measure space,p∈[1,∞),E a real Banach space andf a measurable function:E xT→ℝ. We denote byF the functionalF:
and byDom(F) its domain, it is the set {uεL
p(T,E):ū(t)=f(u),t)εL
1(T)}, and we prove that the sublevelsS(λ)={u:F(u)≤λ} are all connected in the subspaceDom(F) of the Banach spaceL
p(T, E). 相似文献
17.
Michel Talagrand 《Israel Journal of Mathematics》1980,35(1-2):171-176
We construct a Banach spaceE such thatE′ isw
*-separable, andf∈E″/E, which isw
*-continuous on every set ofE′ which is thew
*-closure of a countablebounded set ofE′.
相似文献
18.
M. Edelstein 《Israel Journal of Mathematics》1969,7(1):90-94
LetA be a finite nonempty family of nonempty disjoint closed and bounded sets in a Banach spaceE which is either separable and the conjugate of some Banach spaceX (i.e.E=X*) or, reflexive and locally uniformly convex. IfC denotes the weak*-closed convex hull of ∪ {A:A ∈A} then the set of points inE ∼C through which there is no hyperplane intersecting exactly one member ofA is discrete (or empty).
This research was supported by the National Research Council of Canada, Grant A-3999. 相似文献
19.
Charles Stegall 《Israel Journal of Mathematics》1978,29(4):408-412
A Banach spaceX is an Asplund space (a strong differentiability space) if and only ifX
* has the Radon-Nikodym property. 相似文献
20.
It is shown that a nuclear Fréchet spaceE has the property (DN) if and only if every holomorphic function onE
*, the strongly dual space ofE, with values in the strongly dual space of a Fréchet spaceF having the property (
) can be represented in the exponential form. Moreover, it is shown that the space of holomorphic functions onC
, the space of all complex number sequences, has a linearly absolutely exponential representation system. But the space of holomorphic functions onE
* does not have such a system whenE is a nuclear Fréchet space that does not have the property (DN).Supported by the State Program for Fundamental Researches in Natural Sciences 相似文献