Open AccessAngle in the space of $ p $-summable sequences
Author(s) -
Muh. Nur,
Moch. Idris,
Firman Firman
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022155
Subject(s) - linear subspace , subspace topology , norm (philosophy) , inner product space , mathematics , space (punctuation) , product (mathematics) , combinatorics , vector space , pure mathematics , discrete mathematics , computer science , mathematical analysis , geometry , philosophy , epistemology , operating system
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 $.