On the Commutativity of Closed Symmetric Operators

On the Commutativity of Closed Symmetric Operators

In this paper, we mainly show that if a product AB (or BA ) of a closed symmetric operator A and a bounded positive operator B is normal, then it is self-adjoint. Equivalently, this means that B commutes with A . Certain generalizations and consequences are also presented.

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Veröffentlicht in:Analysis mathematica (Budapest) 2023-09, Vol.49 (3), p.721-731
Hauptverfasser: Dehimi, S., Mortad, M. H., Bachir, A.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Commutativity
Mathematics
Mathematics and Statistics
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Beschreibung
Zusammenfassung:In this paper, we mainly show that if a product AB (or BA ) of a closed symmetric operator A and a bounded positive operator B is normal, then it is self-adjoint. Equivalently, this means that B commutes with A . Certain generalizations and consequences are also presented.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-023-0226-2