Extension Operator for Subspaces of Vector Spaces over the Field \(\mathbb{F}_2\)

IF 0.6 4区 数学 Q3 MATHEMATICS Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI:10.1134/S001626632202006X
O. V. Sipacheva, A. A. Solonkov
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引用次数: 0

Abstract

In is proved that the free topological vector space \(B(X)\) over the field \(\mathbb{F}_2=\{0,1\}\) generated by a stratifiable space \(X\) is stratifiable, and therefore, for any closed subspace \(F\subset B(X)\) (in particular, for \(F=X\)) and any locally convex space \(E\), there exists a linear extension operator \(C(F,E)\to C(B(X),E)\) between spaces of continuous maps.

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域上向量空间子空间的可拓算子 \(\mathbb{F}_2\)
证明了由可分层空间\(X\)生成的域\(\mathbb{F}_2=\{0,1\}\)上的自由拓扑向量空间\(B(X)\)是可分层的,因此,对于任何闭子空间\(F\subset B(X)\)(特别是\(F=X\))和任何局部凸空间\(E\),连续映射空间之间存在一个线性扩展算子\(C(F,E)\to C(B(X),E)\)。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
7
审稿时长
>12 weeks
期刊介绍: Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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