On normal products of selfadjoint operators

IF 0.2 Q3 MATHEMATICS

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

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

引用次数: 14

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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关于自伴随算子的正规积

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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来源期刊

Kyungpook Mathematical Journal MATHEMATICS-

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Kyungpook Mathematical Journal is an international journal devoted to significant research concerning all aspects of mathematics. The journal has a preference for papers having a broad interest. One volume of the journal is published every year. Each volume until volume 42 consisted of two issues; however, starting from volume 43(2003), each volume consists of four issues. Authors should strive for expository clarity and good literary style. Manuscripts should be prepared as follows. The first page must consist of a short descriptive title, followed by the name(s) and address(es) of the author(s) along with an electronic address if available.