Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Normal Products of Selfadjoint Operators

  • Received : 2017.07.07
  • Accepted : 2017.08.26
  • Published : 2017.10.23
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Abstract

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.

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Acknowledgement

Supported by : Kyungpook National University, NCN (National Science Center)

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