实赋范向量空间上多线性映射空间与嵌套组合空间的同构

IF 1 Q1 MATHEMATICS Formalized Mathematics Pub Date : 2022-04-01 DOI:10.2478/forma-2022-0006
Kazuhisa Nakasho, Yuichi Futa
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引用次数: 0

摘要

本文在Mizar[1],[2]中形式化了实赋范空间上由(n + 1)维多线性映射构成的空间与线性映射的n次复合空间之间的等距同构。利用这一结果将Frechet导数的n阶导数空间描述为一个多线性空间。在第1节中,我们讨论了1维多线性映射和0折组合的空间作为准备,在第2节中,我们将讨论扩展到(n + 1)维多线性映射和n折组合的空间。我们在这个形式化中引用了[4]、[11]、[8]、[9]。
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Isomorphism between Spaces of Multilinear Maps and Nested Compositions over Real Normed Vector Spaces
Summary This paper formalizes in Mizar [1], [2], that the isometric isomorphisms between spaces formed by an (n + 1)-dimensional multilinear map and an n-fold composition of linear maps on real normed spaces. This result is used to describe the space of nth-order derivatives of the Frechet derivative as a multilinear space. In Section 1, we discuss the spaces of 1-dimensional multilinear maps and 0-fold compositions as a preparation, and in Section 2, we extend the discussion to the spaces of (n + 1)-dimensional multilinear map and an n-fold compositions. We referred to [4], [11], [8], [9] in this formalization.
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Formalized Mathematics
Formalized Mathematics MATHEMATICS-
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审稿时长
10 weeks
期刊介绍: Formalized Mathematics is to be issued quarterly and publishes papers which are abstracts of Mizar articles contributed to the Mizar Mathematical Library (MML) - the basis of a knowledge management system for mathematics.
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