2018Journal of Mathematical and Computational ScienceOpen access

On bounded n-linear operators

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Abstract

In this paper, the various concepts of bounded and continuous n-linear operators in normed spaces as well as in n-normed spaces are discussed. A sufficient condition for the space of n-linear operators to be a Banach space is given.Further, we prove the equality of two different formulae of norms of an n-linear operator .Also we introduce an n-norm on the dual space of a real linear space.

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What this paper is about

In this paper, the various concepts of bounded and continuous n-linear operators in normed spaces as well as in n-normed spaces are discussed. A sufficient condition for the space of n-linear operators to be a Banach space is given.Further, we prove the equality of two different formulae of norms of an n-linear operator .Also we introduce an n-norm on the dual space of a real linear space.

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Available abstract

In this paper, the various concepts of bounded and continuous n-linear operators in normed spaces as well as in n-normed spaces are discussed. A sufficient condition for the space of n-linear operators to be a Banach space is given.Further, we prove the equality of two different formulae of norms of an n-linear operator .Also we introduce an n-norm on the dual space of a real linear space.

Key concepts: Mathematics, Bounded operator, Normed vector space, Operator norm, Continuous linear operator, Bounded function, Linear operators, Banach space

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