On Normal Products of Selfadjoint Operators

A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator mo...

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Bibliographic Details
Published inKyungpook mathematical journal Vol. 57; no. 3; pp. 457 - 471
Main Authors Jung, Il Bong, Mortad, Mohammed Hichem, Stochel, Jan
Format Journal Article
LanguageKorean
Published 2017
Subjects
Selfadjoint operator
normal operator
unitary polar decomposition
block operator model
normal product
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Summary:A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A, B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.
Bibliography:KISTI1.1003/JNL.JAKO201732663238066
ISSN:1225-6951
0454-8124