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(LF)-空间的完备性 总被引:1,自引:0,他引:1
设(E,ξ)=indlim(E.,ξn)为Frechel空间序列的诱导权限,我们证明了:若每个(Enξ|En)正速完备,则(E,ξ)=indlim(En,ξn)为完备,进而证明了;若对于每个自然数n,存在自然数m(n)使对于任意p≥m(n)有En;则(E,ξ)为完备. 相似文献
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J. M. García-Lafuente 《Monatshefte für Mathematik》1987,103(2):115-120
Once the existence of metrizable (LF)-spaces was discovered, the problem whether the completion of an (LF)-space is or is not an (LF)-space was answered in the negative, because no (LF)-space can be a Fréchet space. However, some (non-metrizable) (LF)-spaces are complete, e.g. the classical Köthe's strict (LF)-spaces. In this paper we will carry out a thorough study of the completeness of (LF)-spaces stressing upon the stable completion properties of (LB)-spaces. A basic tool for handling this problem is an Open Mapping Theorem for completions of (LF)-spaces, which is also proved in the present paper.This research, supported by a Fulbright-MEC fellowship, was carried out during the author's visit at the University of Maryland while on leave from the University of Extremadura. The author is grateful to Professor S. A. Saxon for very helpful conversation and, especially, for calling his attention to the problem of completions of (LF)-spaces. 相似文献
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F. A. Sukochev 《Mathematical Notes》1992,52(6):1280-1282
Translated from Matematicheskie Zametki, Vol. 52, No. 6, pp. 149–151, December, 1992. 相似文献
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Let U be an absolutely convex open subset of a complex barrelled (DF)-space E and let F be a commutative Banach algebra with identity. Let Hb(U, F) be the space of holomorphic mappings from U into F that are bounded on the U-bounded sets and let Hb (U, F) be the space of the holomorphic mappings from U into F that are uniformly weakly continuous on the U-bounded sets, both endowed with the topology τb of uniform convergence on the U-bounded sets. The spectra of (Hwu (U, F), τb) and (Hb(U, F), τb) are studied. 相似文献
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Peter A. Loeb 《Israel Journal of Mathematics》1976,25(1-2):154-187
A solution is given of the generalized Dirichlet problem for an arbitrary compactification of a Brelot harmonic space. A method
of obtaining the Martin-Choquet integral representation of positive harmonic functions is given, and the existence is established
of an ideal boundary Δ supporting the maximal representing measures for positive bounded and quasibounded harmonic functions
with almost all points of Δ being regular for the Dirichlet problem.
This work was supported by a grant from the U. S. National Science Foundation. The results in Sections 1–5 were presented
at the 1974 Oberwolfach Conferences on Potential Theory and Nonstandard Analysis; Sections 1–6 were discussed at the Abraham
Robinson Memorial Conference, Yale, University, May 1975. 相似文献
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An (F)-spaceE is said to be locally midpoint constricted (in short, Imp-constricted) if there exists some>0 such thatD(A/2) <D(A) for every subsetA ofE with 0<D(A), whereD(A) denotes the diameter ofA. Our main result goes as follow: LetE be an Imp-constricted (F)-space andU an open connected subset ofE. Assume thatT:U F is an isometry (i.e., a distance-preserving map) which mapsU onto an open subset of the (F)-spaceF. ThenT can be extended to an affine homeomorphism fromE toF. Also, some other results about the question whether each isometry between two (F)-spaces is affine are obtained. 相似文献
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Jochen Wengenroth 《Results in Mathematics》1997,32(1-2):169-178
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王树泉 《纯粹数学与应用数学》2002,18(4):357-361
通过在S(3)-空间中引入概念θ^2-绝对,建立了S(2)-闭的S(3)-空间与紧空间的联系,并且给出了几个与之相关的性质。 相似文献
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A. Ch. Chigogidze 《Mathematical Notes》1987,41(3):232-234
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Jari Taskinen 《Israel Journal of Mathematics》1995,92(1-3):207-219
We prove a universal mapping theorem for “integral” holomorphic mappings on the open unit ball ofC(K). In our theorem, the universal space isC(K), and the universal mapping is increasing in the positive cone ofC(K). 相似文献
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Susanne Dierolf Leonhard Frerick Elisabetta Mangino Jochen Wengenroth 《manuscripta mathematica》1995,88(1):171-175
Summary In this note we present examples of projective spectraɛ=(E
n
)
n
∈ℕ of (LB)-spaces satisfying proj1 ε≠0 such that the inductive spectrum (E
n
′)
n
∈ℕ of the duals is strict. Moreover, we characterize proj1ε=0 for projective spectra of Moscatelli type.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag 相似文献