Moscow Mathematical Journal

Volume 25, Issue 1, January–March 2025 pp. 63–77.

Converses of Jensen’s and Lah–Ribarič’s Tensorial Inequality for Sequences of Selfadjoint Operators

Authors: Rozarija Mikić (1) and Josip Pečarić (2)
Author institution:(1) Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia
(2) Croatian Academy of Science and Art, Zagreb, Croatia

Summary:

In this paper authors will prove generalization of the Lah–Ribarič inequality for sequences of selfadjoint operators in Hilbert space. They will also give further improvement of the same inequality and bounds for difference between its sides. This improvement will likewise result with more accurate bounds for the gap in the Jensen tensorial inequality for sequences of selfadjoint operators.

2020 Math. Subj. Class. Primary: 47A63; Secondary: 47A80, 26D15.

Keywords: Jensen’s inequality, Edmundson–Lah–Ribarič inequality, convex functions, tensorial product, selfadjoint operators.

Contents Full-Text PDF