Properties of multiplication operators on the space of functions of bounded φ-variation

Abstract

In this paper, the functions u∈BVφ[0,1]u\in B{V}_{\varphi }\left[0,1] which define compact and Fredholm multiplication operators Mu{M}_{u} acting on the space of functions of bounded φ\varphi -variation are studied. All the functions u∈BVφ[0,1]u\hspace{-0.08em}\in \hspace{-0.08em}B{V}_{\varphi }\left[0,\hspace{-0.08em}1] which define multiplication operators Mu:BVφ[0,1]→BVφ[0,1]{M}_{u}:B{V}_{\varphi }\left[0,1]\to B{V}_{\varphi }\left[0,1] with closed range are characterized.

Keywords

• multiplication operator
• bounded variation functions
• compact operators
• fredholm operators
• 47b38
• 26a45
• 26b30
• 46e40