Real Analysis Exchange

Multiplication Operators on the Spaces of Functions of Bounded \(p\)-Variation in Wiener’s Sense

Franklin R. Astudillo-Villaba, René E. Castillo, and Julio C. Ramos-Fernández

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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

Permanent link to this document
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

Subjects
Primary: 26A45: Functions of bounded variation, generalizations 26B30: Absolutely continuous functions, functions of bounded variation 47B38: Operators on function spaces (general)
Secondary: 46E40: Spaces of vector- and operator-valued functions

Keywords
Multiplication Operators p-variation

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


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