Some results on disjointness preserving Fredholm operators between certain Banach function algebras

Mousavi, Lida; Hosseini, Sedigheh

doi:10.30495/maca.2021.1924698.1002

Some results on disjointness preserving Fredholm operators between certain Banach function algebras

https://doi.org/10.30495/maca.2021.1924698.1002

Volume 3, Issue 1
Winter 2021

Pages 32-39

Mathematical Analysis and its Contemporary Applications

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.