ABSTRACT

Let $S=U_S|S|$ and $T=U_T|T|$ be the polar decompositions of S and T in $\mathcal{L}\mathcal{\left(}\mathcal{H}\mathcal{\right)}$, respectively. In this paper we study solutions of operator equations which have similar real and positive parts with both the similarities implemented by a single invertible operator. Moreover, we investigate various properties of such solutions S and T.

中文翻译：

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关于满足实部和正部相似的算子方程的解

摘要

让$\mathrm{小号}={ü}_{\mathrm{小号}}|\mathrm{小号}|$和$吨={ü}_{吨}|吨|$是S和T的极性分解$\mathcal{大号}\mathcal{\left(}\mathcal{H}\mathcal{\right)}$， 分别。在本文中，我们研究了具有相似实部和正部的算子方程的解，它们的相似性由单个可逆算子实现。此外，我们研究了此类解决方案S和T的各种性质。