Operator inequalities and characterizations
Ameur Seddik
TL;DR
This survey explores characterizations of key classes of Hilbert space operators using operator inequalities, including new generalizations for normal operators, enhancing understanding of their structure.
Contribution
It introduces new general characterizations of normal operators and reviews existing characterizations of selfadjoint and unitary operators via operator inequalities.
Findings
New general characterizations for normal operators.
Operator inequalities relate to arithmetic-geometric mean inequality.
Comprehensive survey of operator characterizations.
Abstract
In this survey, we shall present characterizations of some distinguished classes of Hilbertian bounded linear operators (namely, normal operators, selfadjoint operators, and unitary operators) in terms of operator inequalities related to the arithmetic-geometric mean inequality. For the class of all normal operators, we shall present new general characterizations.
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Taxonomy
TopicsHolomorphic and Operator Theory · Mathematical Inequalities and Applications · Analytic and geometric function theory