New inequalities bound the square of the numerical radius w(A) by the norm of an integral average of (t|A| + (1-t)|A*|) squared, itself bounded by half the norm of |A| squared plus |A*| squared.
Some new Karamata type inequalities and their applications to some entropies
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abstract
Some new inequalities of Karamata type are established with a convex function in this paper. The methods of our proof allow us to obtain an extended version of the reverse of Jensen inequality given by Pe{\v} cari\'c and Mi\'ci\'c. Applying the obtained results, we give reverses for information inequality (Shannon inequality) in different types, namely ratio type and difference type, under some conditions. Also, we provide interesting inequalities for von Neumann entropy and quantum Tsallis entropy which is a parametric extension of von Neumann entropy. The inequality for von Neumann entropy recovers the non-negativity and gives a refinement for the weaker version of Fannes's inequality for only special cases. Finally, we estimate bounds for the Tsallis relative operator entropy.
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math.FA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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More accurate numerical radius inequalities
New inequalities bound the square of the numerical radius w(A) by the norm of an integral average of (t|A| + (1-t)|A*|) squared, itself bounded by half the norm of |A| squared plus |A*| squared.