2024 AOFA Best Paper Award Webinar by Prof. G. Ramesh
Prof G. Ramesh
Having completed M. Sc degree in Mathematics from the Hyderabad Central University in 2002, Dr. G. Ramesh went on to pursue his research in Operator Theory and graduated Ph. D from IIT Madras in 2008. He joined as an Assistant Professor in the department of Mathematics at IIT Hyderabad in 2011 after two years of Postdoctoral studies at the Indian Statistical Institute, Bangalore. Currently, he is working as a Professor in the same institute.
His principle research exploration revolves around operator theory, specifically the spectral theory of operators that are bounded as well as unbounded. For the last few years, he has been working on developing the spectral theory of absolutely norm attaining operators, absolutely minimum attaining operators (both bounded and unbounded ones). These classes are introduced with the aim of solving the invariant subspace problem (for a class of operators), which is a longstanding open problem. Quaternionic Operator Theory and C-Normal Operators are some other topics that he work on.
Abstract
In this talk, first, we discuss the spectral properties of operators that attain their norm on every reducing subspace. Next, we explore the structure of normal and quasinormal operators in this class. At the end, we describe paranormal operators whose adjoint is also paranormal. This gives direct proof of the fact that an operator is normal if and only if the operator and its adjoint are paranormal.
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Annals of Functional Analysis
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