Abstract
\( \newcommand\norm[1]{\left\lVert#1\right\rVert}\newcommand\normx[1]{\left\Vert#1\right\Vert} \)In this paper several tensorial norm inequalities for continuous functions of selfadjoint operators in Hilbert spaces have been obtained. Multiple inequalities are obtained with variations due to the convexity properties of the mapping $f$$$\norm{(1\otimes B-A\otimes 1)^{-1}[\operatorname{exp}(1\otimes B)-\operatorname{exp}(A\otimes 1)]- \operatorname{exp}\left(\frac{A\otimes 1+1\otimes B}{2}\right)}$$$$\leqslant \norm{1\otimes B-A\otimes 1}^{2}\frac{\norm{f''}_{I,+\infty}}{24}.$$
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have