We give the necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss the structure of such operators in the case of self-adjoint and normal operators separately. Finally, we discuss several properties of absolutely norm attaining operators. © 2019, Indian Academy of Sciences.

Venku Naidu .D

Department of Mathematics

Ramesh G

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Indian Institute of Technology Hyderabad (IITH) is a premier institute of science and technology established in 2008. IITH has been consistently ranked in the&nbsp;<a href="https://iith.ac.in/reports/" rel="noopener noreferrer">top 10 institutes</a>&nbsp;in India for Engineering&nbsp;<a href="https://www.nirfindia.org/2021/EngineeringRanking.html" rel="noopener noreferrer" target="_blank">according to NIRF</a>&nbsp;making it one of the most coveted schools for science and technology in the country.

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Journal	Data powered by TypesetProceedings of the Indian Academy of Sciences: Mathematical Sciences
Publisher	Data powered by TypesetSpringer
ISSN	02534142