关于自伴随算子的正规积

Pub Date : 2017-01-01 DOI:10.5666/KMJ.2017.57.3.457

I. Jung, M. H. Mortad, J. Stochel

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引用次数: 14

摘要

给出了自伴随算子A与有界自伴随算子B的乘积AB为正规的充分必要条件。在AB为正积的情况下，得到了A和B的酉极分解因子的各种性质。建立了自伴随算子对(A,B)的块算子模型，其中B是有界的，AB是正规的。讨论了算子A和算子B都有界的情况。此外，从这个角度重新审视了里德的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 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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