2024/02/21 by Mohammad Sababheh, Hamid Reza Moradi, Sababheh, Mohammad +5
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2402.13479
openalex publication_date 2024/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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× 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.