Student Success Story

Functional Analysis contributes to the development of operator theory

Prof. Kangyong LEE, Chungnam National University

His goal is to contribute to the development of Functional Analysis (operator theory) with the research on quasi-AW*-algebras


Professor Kangyong LEE was appointed as the assistant professor at Chungnam National University in March 2017 after finishing his degree in SKKU and Ohio State University. He was also at SKKU as a research professor under the President’s Postdoctoral Fellowship.

He pointed his research on Module Theory asthe main reason for his appointment. When he was studying at Ohio State University, he wrote numerous theses on the Module Theory after being guided by his professor Tariq Rizvi.

Secondly, he said it was thanks to the examiners who selected him for the President’s Postdoctoral Fellowship. His research topic in 2014 was about the endomorphism ring. The fact that he can use the research funds from the fellowship even after the appointment was one of the key factors. He said that writing a research plan as a mathematics major was difficult but he was able to be selected for the fellowship thanks to the support and the promotion of SKKU.

Third, his experience as an adjunct professor at Hanyang University was also one of the factors. Chungnam National University’s department of mathematics education emphasize teaching experience as it is a teacher’s college. 

Prof LEE researches on the module. Module is simply the common term of vector space. Module is the expansion of the vector space on the field to the ring. In 2004, professor Rizvi and Roman from Ohio State University started researching about the characteristic of the module with its correlation with the endomorphism ring. 

Endomorphism is an important tool for the research in Group Theory and Operator Theory and it has a very close relationship with the module in the Module Theory. Research on modules using endomorphism began long time ago but it was only after 2004 that the foundation was established. Prof LEE began defining Rickart modules, Dual Rickart modules, L-Rickart modules, Endoregular modules, Unit-endoregular modules using the endomorphism after he met Prof Rizvi in 2007 at the Ohio State University. He also researched on the various characteristics of the listed modules.

Prof LEE proved that it has an organic relationship with modules that had been researched in the past and created the Characterization Theorem. His task is to carry on and develop the theories made by Prof Rizvi and Roman. His current research topic on the quasi-Baer modules is also a module defined by endomorphism and it has a critical role in his President’s Postdoctoral Fellowship assignment. The quasi-Baer has been proven by Birkenmeier, Park and Rizvi in 2009 that it has a very close relationship with the functional analysis as an algebraic part of the AW*-algebra. He is trying to contribute towards the development of operator theory by researching AW*-algebras.

Prof LEE said that he received many help from different people to be selected as the President's Postdoctoral fellow. “I would like to express my gratitude to the examiners who foresaw the value of my research. My last presentation was in English and my colleagues gave me many feedbacks. My academic advisor Prof Mikyung KIM gave me lot of support.”

In 2009, a thesis connecting quasi-Baerrings and C*-algebras was researched by his academic advisor and Prof Jaegul PARK of Pusan National University. His goal is to continue the research. Also, he plans to develop the module theory proposed by his academic advisor in 2004.

Generally, most of the outcomes produced by mathematicians disappear within 10 years. His dream is to produce an outcome that will be used by the younger generation for more than 50 years.