Multiplication operators on the space of functions of bounded variation

Abstract

In this paper,we study the properties of the multiplication operator acting on the bounded variation space BV[0, 1]. In particular,we show the existence of non-null compact multiplication operators on BV[0, 1] and non-invertible Fredholm multiplication operators on BV[0, 1].

Keywords

• Multiplication operator
• Functions of bounded variation
• Primary 26B30
• 47B38
• Secondary 46E40