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arXiv · 2402.13479

Some inequalities for adjointable operators on Hilbert $C^*$-modules

Mohammad Sababheh·Hamid Reza Moradi·Qingxiang Xu·Shuo Zhao
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Abstract

The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator norm as well as the numerical radius, respectively. Among other things, the positivity of a $2\times 2$ block operator matrix is clarified without any preconditions on its entries, and a generalized version of the mixed Schwarz inequality with a parameter is derived. Numerical examples are provided to illustrate the non-triviality of this newly obtained inequality.

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Mohammad Sababheh, Hamid Reza Moradi, Qingxiang Xu, Shuo Zhao. 2024-02-21. Some inequalities for adjointable operators on Hilbert $C^*$-modules. https://arxiv.org/abs/2402.13479

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