A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz inequality in elementary courses. Several consequences are proved in a way which allow an elementary proof of strong subadditivity in a few more lines. Some ...

Some new results that provide refinements and reverses of the Cauchy-Bunyakovsky-Schwarz (CBS)−inequality in the general setting of Measure Theory and under some boundedness conditions for the functions involved are given.

In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.

The squeezing and violation of the Cauchy-Schwarz inequality in the fluorescent field of collective double resonant process are discussed. J. Physique 48 (1987) 1925-1931 NOVEMBRE 1987, Classification Physics Abstracts 42.50

An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.

Some new reverses of the Cauchy-Bunyakovsky-Schwarz integral inequality for vector-valued functions in Hilbert spaces that complement the recent results obtained in [1] are given. Applications for the Heisenberg inequality are provided.