ON THE MATRIX CAUCHY-SCHWARZ INEQUALITY

SABABHEH, MOHAMMAD; CONDE, CRISTIAN; MORADI, HAMID REZA

OPERATORS AND MATRICES

ELEMENT

Lugar: Zagreb; Año: 2023 vol. 17 p. 525 - 538

1846-3886

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 cameas an umbrella of Cauchy-Schwarz-like inequalities, then we consider the mixed Cauchy-Schwarzinequality. This latter inequality has been influential in obtaining several other matrix inequalities, including numerical radius and norm results. Among many other results, it has beenshown that|T| ≤ 1/4(| |T| + |T^*| + 2R(T)| + | |T| + |T^*| − 2R(T)|).where R(T) is the real part of T.