## Real Analysis Exchange

### Multiplication Operators on the Spaces of Functions of Bounded $p$-Variation in Wiener’s Sense

#### Abstract

In this article, we make a comprehensive study of the properties of multiplication operators acting on the spaces of functions of bounded $p$-variation in Wiener’s sense, $WBV_p[0,1]$. We characterize all functions $u\in WBV_p[0,1]$ that define invertible, compact and Fredholm multiplication operators $M_u$ on $WBV_p[0,1]$. Also we characterize when $M_u$ has finite range and has closed range on $WBV_p[0,1]$.

#### Article information

Source
Real Anal. Exchange, Volume 42, Number 2 (2017), 329-344.

Dates
First available in Project Euclid: 10 May 2018

https://projecteuclid.org/euclid.rae/1525917691

Digital Object Identifier
doi:10.14321/realanalexch.42.2.0329

Mathematical Reviews number (MathSciNet)
MR3721805

Zentralblatt MATH identifier
06870333

#### Citation

Astudillo-Villaba, Franklin R.; Castillo, René E.; Ramos-Fernández, Julio C. Multiplication Operators on the Spaces of Functions of Bounded $p$-Variation in Wiener’s Sense. Real Anal. Exchange 42 (2017), no. 2, 329--344. doi:10.14321/realanalexch.42.2.0329. https://projecteuclid.org/euclid.rae/1525917691