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Multi-generalized 2-normed space

Mahnaz Khanehgir, Marzieh Moradian Khibary, Firoozeh Hasanvand, Ahmad Modabber

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Abstract

In this paper, we introduce the concepts of multi-generalized 2-normed space and dual multigeneralized 2-normed space and we then investigate some results related to them. We also prove that, if (E,||.,.||) is a generalized 2-normed space, {||.,.||k}k?N is a sequence of generalized 2-norms on Ek (k ? N) such that for each x,y ? E, ||x,y||1 = ||x,y|| and for each k ? N axioms (MG1), (MG2) and (MG4)((DG4)) of (dual) multi-generalized 2-normed space are true, then {(Ek,||.,. ||k), k ? N} is a (dual) multi-generalized 2-normed space. Finally we deal with an application of a dual multi-generalized 2-normed space defined on a proper commutative H*-algebra.

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What this paper is about

In this paper, we introduce the concepts of multi-generalized 2-normed space and dual multigeneralized 2-normed space and we then investigate some results related to them. We also prove that, if (E,||.,.||) is a generalized 2-normed space, {||.,.||k}k?N is a sequence of generalized 2-norms on Ek (k ? N) such that for each x,y ? E, ||x,y||1 = ||x,y|| and for each k ? N axioms (MG1), (MG2) and (MG4)((DG4)) of (dual) multi-generalized 2-normed space are true, then {(Ek,||.,. ||k), k ? N} is a (dual) multi-generalized 2-normed space. Finally we deal with an application of a dual multi-generalized 2-normed space defined on a proper commutative H*-algebra.

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Available abstract

In this paper, we introduce the concepts of multi-generalized 2-normed space and dual multigeneralized 2-normed space and we then investigate some results related to them. We also prove that, if (E,||.,.||) is a generalized 2-normed space, {||.,.||k}k?N is a sequence of generalized 2-norms on Ek (k ? N) such that for each x,y ? E, ||x,y||1 = ||x,y|| and for each k ? N axioms (MG1), (MG2) and (MG4)((DG4)) of (dual) multi-generalized 2-normed space are true, then {(Ek,||.,. ||k), k ? N} is a (dual) multi-generalized 2-normed space. Finally we deal with an application of a dual multi-generalized 2-normed space defined on a proper commutative H*-algebra.

Key concepts: Normed vector space, Mathematics, Normed algebra, Dual norm, Strictly convex space, Space (punctuation), Axiom, Dual (grammatical number)

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