2022/05/05 by Mohammad Sababheh, Sababheh, Mohammad, Cristian Conde +3
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Mathematics and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2205.02657
openalex publication_date 2022/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main goal of this work is to present new matrix inequalities of the Cauchy-Schwarz type. In particular, we investigate the so-called Lieb functions, whose definition came as an umbrella of Cauchy-Schwarz-like inequalities, then we consider the mixed Cauchy-Schwarz inequality. This latter inequality has been influential in obtaining several other matrix inequalities, including numerical radius and norm results. Among many other results, we show that ‖ T ‖≤ (1)/(4)( ‖ | T |+| T* |+2\mathfrak RT ‖+‖ | T |+| T* |-2\mathfrak RT ‖ ), where \mathfrak RT is the real part of T.