c-Algebrability of Pathological Sets of Product Integrable Functions

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Fateme Farmanesh, Ali Farokhinia, c-Algebrability of Pathological Sets of Product Integrable Functions, Int. J. Anal. Appl., 16 (5) (2018), 702-711.

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Fateme Farmanesh, Ali Farokhinia

Abstract

In this paper we investigate linear algebraic structures in the set of product integrable matrix-valued functions and find $\mathfrak{c}$-generated algebras in $L([a,b],{{\mathbb{R}}^{n\times n}})\backslash {{L}^{*}}([a,b],{{\mathbb{R}}^{n\times n}})$ and $D([a,b],{{\mathbb{R}}^{n\times n}})\backslash {{L}}([a,b],{{\mathbb{R}}^{n\times n}})$.

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