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BY 4.0 license Open Access Published by De Gruyter Open Access July 22, 2020

Some integral inequalities for operator monotonic functions on Hilbert spaces

  • Silvestru Sever Dragomir EMAIL logo
From the journal Special Matrices


Let f be an operator monotonic function on I and A, BI (H), the class of all selfadjoint operators with spectra in I. Assume that p : [0.1], →ℝ is non-decreasing on [0, 1]. In this paper we obtained, among others, that for A ≤ B and f an operator monotonic function on I,


in the operator order.

Several other similar inequalities for either p or f is differentiable, are also provided. Applications for power function and logarithm are given as well.

MSC 2010: 47A63; 26D15; 26D10


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Received: 2020-05-06
Accepted: 2020-06-24
Published Online: 2020-07-22

© 2020 Silvestru Sever Dragomir, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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