A New Semi-Inner Product and p n -Angle in the Space of p -Summable Sequences

Muh Nur (), Mawardi Bahri, Anna Islamiyati and Harmanus Batkunde
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Muh Nur: Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia
Mawardi Bahri: Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia
Anna Islamiyati: Department of Statistics, Hasanuddin University, Makassar 90245, Indonesia
Harmanus Batkunde: Department of Mathematics, Pattimura University, Ambon 97233, Indonesia

Mathematics, 2023, vol. 11, issue 14, 1-13

Abstract: In this paper, we propose a definition for a semi-inner product in the space of p -summable sequences equipped with an n -norm. Using this definition, we introduce the concepts of p n -orthogonality and the p n -angle between two vectors in the space of p -summable sequences. For the special case n = 1, these concepts are identical to previous studies. We also introduce the notion of the p n -angle between one-dimensional subspaces and arbitrary-dimensional subspaces. The authors believe that the results obtained in this paper are very significant, especially in the theory of n -normed space in functional analysis.

Keywords: semi-inner product; p n -orthogonality; p n -angle; n -norm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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