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

Multi-generalized 2-normed space. (English) Zbl 1488.46045

Filomat 31, No. 3, 841-851 (2017).
Summary: In this paper, we introduce the concepts of multi-generalized 2-normed space and dual multi-generalized 2-normed space and we then investigate some results related to them. We also prove that, if \((E,\|.,.\|)\) is a generalized 2-normed space, \(\{\|.,.\|\}_{k\in\mathbb{N}}\) is a sequence of generalized 2-norms on \(E^k\) \((k\in\mathbb{N})\) such that for each \(x,y\in E\), \(\|x,y\|_1=\|x,y\|\) and for each \(k\in\mathbb{N}\) axioms \((MG1),(MG2)\) and \((MG4)(\ (DG4))\) of (dual) multi-generalized 2-normed space are true, then \(\{(E^k,\|.,.\|_k),k\in\mathbb{N}\}\) 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.

MSC:

46B99 Normed linear spaces and Banach spaces; Banach lattices

Keywords:

generalized 2-normed space; (dual) multi-normed space; (dual) multi-generalized 2-norm; special generalized 2-norm
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References:

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