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2023•Journal of Southwest Jiaotong UniversityOpen access

A NOTE ON THE N-NORM OF A NORMED SPACE

Muh Nur, Mawardi Bahri, Amir Kamal Amir, Anna Islamiyati, Muh Nur, Mawardi Bahri, Amir Kamal Amir, Anna Islamiyati

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Abstract

It is known that a normed space can be equipped with several -norms. Geometrically, -norm is interpreted as the volume of the -dimensional parallelepiped that is spanned by vectors. In this article, we propose a new -norm related to the semi-inner product in the normed space. The results are generalizations for and different from the existing -norms. We also investigate its relation to at least one of the -norms defined previously by Nur and Gunawan. Additionally, we show that the new -norm and the standard -norm are identical on an inner product space. Keywords: Normed Space, -Norm, Semi-Inner Product g DOI： https://doi.org/10.35741/issn.0258-2724.58.2.38

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It is known that a normed space can be equipped with several -norms. Geometrically, -norm is interpreted as the volume of the -dimensional parallelepiped that is spanned by vectors. In this article, we propose a new -norm related to the semi-inner product in the normed space. The results are generalizations for and different from the existing -norms. We also investigate its relation to at least one of the -norms defined previously by Nur and Gunawan. Additionally, we show that the new -norm and the standard -norm are identical on an inner product space. Keywords: Normed Space, -Norm, Semi-Inner Product g DOI： https://doi.org/10.35741/issn.0258-2724.58.2.38

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Available abstract

It is known that a normed space can be equipped with several -norms. Geometrically, -norm is interpreted as the volume of the -dimensional parallelepiped that is spanned by vectors. In this article, we propose a new -norm related to the semi-inner product in the normed space. The results are generalizations for and different from the existing -norms. We also investigate its relation to at least one of the -norms defined previously by Nur and Gunawan. Additionally, we show that the new -norm and the standard -norm are identical on an inner product space. Keywords: Normed Space, -Norm, Semi-Inner Product g DOI： https://doi.org/10.35741/issn.0258-2724.58.2.38

Key concepts: Inner product space, Normed vector space, Norm (philosophy), Dual norm, Mathematics, Parallelepiped, Space (punctuation), Normed algebra

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