Angle in the space of $ p $-summable sequences

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-16 DOI:10.3934/math.2022155

M. Nur, M. Bahri, A. Islamiyati, Harmanus Batkunde

引用次数: 0

Abstract

The aim of this paper is to investigate completness of $ A $ that equipped with usual norm on $ p $-summable sequences space where $ A $ is subspace in $ p $-summable sequences space and $ 1\le p < \infty $. We also introduce a new inner product on $ A $ and prove completness of $ A $ using a new norm that corresponds this new inner product. Moreover, we discuss the angle between two vectors and two subspaces in $ A $. In particular, we discuss the angle between $ 1 $-dimensional subspace and $ (s-1) $-dimensional subspace where $ s\ge 2 $ of $ A $.

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$ p $-可和序列空间中的角

本文的目的是研究具有通常范数的$ A $在$ p $ -可和序列空间上的完备性，其中$ A $是$ p $ -可和序列空间和$ 1\le p < \infty $中的子空间。在$ A $上引入了一个新的内积，并用一个新的范数证明了$ A $的完备性。此外，我们还讨论了$ A $中两个向量与两个子空间之间的夹角。特别地，我们讨论了$ 1 $维子空间与$ (s-1) $维子空间之间的夹角，其中$ A $的$ s\ge 2 $。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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