Abstract

In this paper, we relate composition operators with multiplication operators on the general Banach function spaces on a $\sigma$-finite measure space. We use this relation to study the invertibility and Fredholmness properties of composition operators on the Banach function spaces.

Keywords: Banach function spaces, closed range, composition operators, Fredholm operator, invertibility, measurable transformation.

MSC: 47B33, 46E30, 47B07, 46B70

Pages:  97$-$111     

Volume  59 ,  Issue  3 ,  2007