Document Type : Original Article

Authors

• Lida Mousavi ¹
• Sedigheh Hosseini ²

¹ Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran

² Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.

Abstract

For two algebras $\A$ and $\B$, a linear map $T : \A \lo \B$ is disjointness preserving if $x \cdot y = 0$ implies $Tx \cdot Ty = 0$ for all $x, y \in \A$ and is said Fredholm if dim(ker($T$)) i.e. the  nullity of $T$ and codim($T(E)$) i.e. the corank of $T$ are finite. We develop some results of  Fredholm linear disjointness preserving operators from $C_0(X)$ into $C_0(Y)$ for locally compact  Hausdorff spaces $X$ and $Y $in \cite{JW28}, into regular Banach function algebras. In particular,  we consider weighted composition Fredholm operators as a typical example of disjointness preserving  Fredholm operators on certain regular Banach function algebras.