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 $.
Citation: Muh Nur, Moch Idris, Firman. Angle in the space of $ p $-summable sequences[J]. AIMS Mathematics, 2022, 7(2): 2810-2819. doi: 10.3934/math.2022155
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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Muh Nur, Moch Idris, Firman. Angle in the space of $ p $-summable sequences[J]. AIMS Mathematics, 2022, 7(2): 2810-2819. doi: 10.3934/math.2022155
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