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Simpson Type Tensorial Norm Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Stojiljković, Vuk 

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In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities of the form

    \[\bigg|\bigg|\frac{1}{3}\left(2\operatorname{exp}\left(A\right)\otimes 1-\operatorname{exp}\left(\frac{A\otimes 1 +1\otimes B}{2}\right)+2\cdot 1\otimes \operatorname{exp}\left(B\right)\right)\]

    \[-(1\otimes B-A\otimes 1)^{-1}\times\bigg(\operatorname{exp}(1\otimes B)-\operatorname{exp}(A\otimes 1)\bigg)\bigg|\bigg|\]

    \[\leqslant \norm{1\otimes B-A\otimes 1}\frac{5}{12}\operatorname{exp}(M)\]

are obtained with variations due to the convexity properties of the mapping f.

 

 

 

 

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Stojiljković, Vuk 

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