Spaceability and algebrability of the set of non strongly McShane (product) integrable functions

Authors

  • Ali Farokhinia Dept. of Math. Shiraz Branch, Islamic Azad University
  • Fatemeh Farmanesh Dept. of Math. Shiraz Branch, Islamic Azad University

DOI:

https://doi.org/10.30495/jme.v14i0.989

Keywords:

Spaceability, Algebrability, McShane integrable, Product integrable

Abstract

Let X be a unitial Banach algebra, G be the set of functions f : [0, 1] → X that are non strongly McShane integrable and L be the set of functions f : [0, 1] → [0, ∞) that are non strongly McShane integrable. The aim of this paper is to show that there is an infinite dimensional closed vector space in G ∪0 and a c-generated algebra in L isomorphic with a free algebra.

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Published

2019-04-10

Issue

Vol. 14

Section

Vol. 14, No. 2, (2020)

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