On Absolutely Norm attaining Operators
G. Ramesh, D. Venku Naidu
TL;DR
This paper characterizes absolutely norm attaining operators between complex Hilbert spaces, providing conditions and exploring their structure, especially for self-adjoint and normal operators, along with their properties.
Contribution
It offers necessary and sufficient conditions for absolutely norm attaining operators and analyzes their structure in special cases, advancing understanding of these operators.
Findings
Characterization of absolutely norm attaining operators
Structural analysis for self-adjoint and normal cases
Discussion of properties of such operators
Abstract
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately. Finally, we discuss several properties of absolutely norm attaining operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Mathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics