Some results around quadratic maps

Abstract

This paper dedicated to study quadratic maps. We present some new operator equalities and inequalities by using quadratic map in the framework of B(H). Applications for particular case of interest are also provided. The parallelogram law is recovered  and some other interesting operator equalities are established. Afterward,   we get an extension of some well known inequalities such as, triangle  inequality. Especially, Bohr's inequality is generalized to the context of quadratic map. Some results concerning this inequality are surveyed.  We give an application of our results in the previous sections. We show that our results are a generalization of some well known works due to Fujii and Hirzallah.

Keywords

• "Quadratic map
• operator inequalities
• absolute value

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