Strong Algebrability of Certain  Subset of C_0 (X)

Ali Tond; Ali Farokhinia

Ali Tond Dept. of Mathematics, Assistant Professor at Shiraz Branch, Islamic Azad University, Iran
Ali Farokhinia Dept. of Mathematics, Assistant Professor at Shiraz Branch, Islamic Azad University, Iran

Keywords: Strong Algebrability, Pathological Properties, Free Algebra.

Abstract

In 2013, strong algebrability of 𝑐₀ ∖∪𝑝 ℓ ^𝑝 is proved by Bartoszewics and Glab. In this paper we expand this result to an arbitrary finite dimensional Banach space. The main theorem of this paper concerns that 𝐶₀ (𝑋) ∖∪𝑝 𝐿^𝑝 (𝑋) contains an infinitely generated free algebra, where 𝑋 is a finite dimensional Banach space.

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