## Pompeiu-Čebyšev type inequalities for selfadjoint operators in Hilbert spaces.(English)Zbl 06902446

Summary: In this work, generalizations of some inequalities for continuous $$h$$-synchronous ($$h$$-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved.

### MSC:

 47A63 Linear operator inequalities 47A99 General theory of linear operators

### Keywords:

Hilbert space; selfadjoint operators; $$h$$-synchronization
Full Text:

### References:

 [1] M. W. Alomari, On Pompeiu-Chebyshev functional and its generalization, Preprint arXiv:1706.06250v2. · Zbl 1408.26018 [2] S. S. Dragomir, Čebyšev’s type inequalities for functions of selfadjoint operators in Hilbert spaces, Linear Multilinear Algebra, 58 no 7-8 (2010), 805-814. [3] S. S. Dragomir, Operator inequalities of the Jensen, Čebyšev and Grüss type, Springer, New York, 2012. · Zbl 1242.47001 [4] T. Furuta, J. Mićić, J. Pečarić, and Y. Seo, Mond-Pečarić method in operator inequalities. Inequalities for bounded selfadjoint operators on a Hilbert space, Element, Zagreb, 2005. · Zbl 1135.47012 [5] M. S. Moslehian and M. Bakherad, Chebyshev type inequalities for Hilbert space operators, J. Math. Anal. Appl. 420 (2014), no. 1, 737-749. · Zbl 1311.47021 [6] J. S. Matharu and M. S. Moslehian, Grüss inequality for some types of positive linear maps, J. Operator Theory 73 (2015), no. 1, 265-278. · Zbl 1389.47057
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