Douglas' plus Sebestyen's lemmas = a tool for solving an operator equation problem
Douglas' plus Sebestyen's lemmas = a tool for solving an operator equation problem
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道格拉斯 (Douglas) 加上 Sebestyen 引理 = 求解算子方程问题的工具
DOI：
10.1016/j.jmaa.2019.123599
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发表时间：
2020
影响因子：
1.3
通讯作者：
Xu Qingxiang
中科院分区：
文献类型：
--
作者：
Cvetkovic-Ilic Dragana;Wang Qing-Wen;Xu Qingxiang
在不同的条件下，考虑了方程AX B= C的正解的存在性，但仅在包括正则性条件在内的附加条件下，以及在一定范围的条件下，如R（B）R（A）.在本文中，我们考虑这个开放的问题，并提出了一些等价的存在性的正解的算子方程AX B= C没有任何额外的范围的假设使用两个著名的结果道格拉斯和Sebestyén。同时，我们也考虑了正解的一般形式。
The existence of a positive solution of the equation A X B= C was considered in different settings but only under additional conditions including that of regularity, as well as under certain range conditions such as R (B)⊆ R (A⁎)‾. In this paper we consider this open question and present some equivalents of the existence of a positive solution of the operator equation A X B= C without any additional range assumptions using two well-known results of Douglas and Sebestyén. Also we consider a general form of a positive solution.