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2023•European Journal of Pure and Applied MathematicsOpen access

Inner Products on Discrete Morrey Spaces

Muhammad Jakfar, Manuharawati Manuharawati, Agung Lukito, Shofan Fiangga

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Abstract

The discrete Morrey space m_(u,p) is a generalization of the p-summable sequence space l^p. We have known that the space is a normed space, but the space m_(u,p) equipped with the usual norm is not an inner product space for p is not equal to 2. In this paper, we shall show that this space is actually contained in an inner product space. That means this space equipped with the inner product is an inner product space. The relationship between a standard norm on and the inner product is studied.

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What this paper is about

The discrete Morrey space m_(u,p) is a generalization of the p-summable sequence space l^p. We have known that the space is a normed space, but the space m_(u,p) equipped with the usual norm is not an inner product space for p is not equal to 2. In this paper, we shall show that this space is actually contained in an inner product space. That means this space equipped with the inner product is an inner product space. The relationship between a standard norm on and the inner product is studied.

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Available abstract

The discrete Morrey space m_(u,p) is a generalization of the p-summable sequence space l^p. We have known that the space is a normed space, but the space m_(u,p) equipped with the usual norm is not an inner product space for p is not equal to 2. In this paper, we shall show that this space is actually contained in an inner product space. That means this space equipped with the inner product is an inner product space. The relationship between a standard norm on and the inner product is studied.

Key concepts: Inner product space, Mathematics, Space (punctuation), Norm (philosophy), Normed vector space, Product (mathematics), Generalization, Product topology

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