2020•Electronics Science Technology and ApplicationOpen access

Bounded and Continuous Linear Operators on Linear 2-Normed Space

Raghad I. Sabri

Abstract

In this article, at first basic definitions and properties of linear 2-normed space are presented. Then the author defines bounded operator as an introduction to defined norm of an operator. In addition, the definition of continuous operator on a linear 2-normed space is given. This article proved an operator Γ from a linear 2-normed space (U,〖||.||〗_U) into a linear 2-normed space (V, 〖||.||〗_V) is bounded operator if and only if Γ is continuous operator.

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Key concepts: Continuous linear operator, Bounded operator, Normed vector space, Operator norm, Mathematics, Bounded function, Finite-rank operator, Operator space