Theoretical study demonstrates generalized normal operator properties in Hilbert spaces, extending classical polar decomposition and Bohr's inequality.
In this paper, a generalization of normal operators in Hilbert spaces is introduced. Specifically, a bounded linear operator T on a complex Hilbert space \(H\) as \([P]\) -normal if \(T*PT = TPT*\) is defined, where \(P\) is a bounded positive linear operator on \(H\) , and \(T*\) denotes the adjoint operator of T . Several properties and characterizations involving this new class of operators are examined. Additionally, the \(P\) -absolute value in semi-Hilbert spaces is introduced, and several applications are presented, including a generalization of the polar decomposition and Bohr’s inequality for Hilbert space operators. Other related results are also discussed.
No takes yet. Share an insight, caveat, or question.
Najla Altwaijry (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: