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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Muh Nur & Mawardi Bahri & Anna Islamiyati & Harmanus Batkunde, 2023. "A New Semi-Inner Product and p n -Angle in the Space of p -Summable Sequences," Mathematics, MDPI, vol. 11(14), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3139-:d:1195192
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