Twice Differentiable Ostrowski Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Authors

  • Vuk Stojiljkovic

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4843

Keywords:

Tensorial product, Selfadjoint operators, Convex functions

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 $f$
$$\norm{(1\otimes B-A\otimes 1)^{-1}[\operatorname{exp}(1\otimes B)-\operatorname{exp}(A\otimes 1)]- \operatorname{exp}\left(\frac{A\otimes 1+1\otimes B}{2}\right)}$$
$$\leqslant \norm{1\otimes B-A\otimes 1}^{2}\frac{\norm{f''}_{I,+\infty}}{24}.$$

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Published

2023-07-30

Issue

Section

Nonlinear Analysis

How to Cite

Twice Differentiable Ostrowski Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1421-1433. https://doi.org/10.29020/nybg.ejpam.v16i3.4843

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