The Noncommutative Singer-Wermer Conjecture and Generalized Skew Derivations

Feng Wei*, Jing Xiong Xu

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The noncommutative Singer-Wermer conjecture states that every linear derivation on a noncommutative Banach algebra maps into its Jacobson radical. This conjecture is still an open question for more than thirty years. In this paper, the question of when a generalized skew derivation on a Banach algebra has quasinilpotent values is considered and how this question is related to the noncommutative Singer-Wermer conjecture is discussed.

Original languageEnglish
Title of host publicationAdvances in Ring Theory and Applications - WARA22
EditorsShakir Ali, Mohammad Ashraf, Nadeem ur Rehman, Vincenzo De Filippis
PublisherSpringer
Pages189-206
Number of pages18
ISBN (Print)9783031507946
DOIs
Publication statusPublished - 2024
EventWorkshop on Associative Rings and Algebras with Additional Structures, WARA 2022 - Messina, Italy
Duration: 18 Jul 202220 Jul 2022

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume443
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceWorkshop on Associative Rings and Algebras with Additional Structures, WARA 2022
Country/TerritoryItaly
CityMessina
Period18/07/2220/07/22

Keywords

  • Banach algebra
  • Generalized skew derivation
  • Singer-wermer conjecture

Fingerprint

Dive into the research topics of 'The Noncommutative Singer-Wermer Conjecture and Generalized Skew Derivations'. Together they form a unique fingerprint.

Cite this