Some Cauchy-Bunyakovsky-Schwarz Type Inequalities for Sequences of Operators in Hilbert Spaces

Reverse Cauchy--Schwarz inequalities for positive C*-valued sesquilinear forms

We prove two new reverse Cauchy--Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C*-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy--Schwarz inequality due to G Polya and G. Szego.

A treatment of the Cauchy--Schwarz inequality in $C^*$-modules

We study the Cauchy--Schwarz and some related inequalities in a semi-inner product module over a $C^*$-algebra $\A$. The key idea is to consider a semi-inner product $\A$-module as a semi-inner product $\A$-module with respect to another semi-inner product. In this way, we improve some inequalities such as the Ostrowski inequality and an inequality related to the Gram matrix. The induced semi-inner products are also related to the the notion of covariance and variance. Furthermore, we obtain a sequence of nested inequalities that emerges from the Cauchy--Schwarz inequality. As a consequence, w…

非交换Lp空间中映射的柯西-施瓦茨不等式

Cauchy-Schwarz inequalities for maps in noncommutative Lp-spaces

本文研究了非交换Lp空间中正半线性映射的广义柯西-施瓦茨不等式，推导了实部和虚部的界估计，并在非交换L2空间中推广了不确定性关系。还提出了非交换L2空间的新范数，并证明了正半线性映射的柯西-施瓦茨不等式。

Operator inequalities related to weak 2-positivity

In this paper we introduce the notion of weak 2-positivity and present some examples. We establish some operator Cauchy--Schwarz inequalities involving the geometric mean and give some applications. In particular, we present some operator versions of Hua's inequality by using the Choi--Davis--Jensen inequality.