Dragomir, Sever Silvestru; Mond, Bertram; Pečarić, Josip E. On Jensen’s inequality for self-adjoint operators in Hilbert space. (English) Zbl 0857.47010 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 34, 7-13 (1995). Summary: Some inequalities, related to Jensen’s discrete inequality, are given for selfadjoint operators in Hilbert space. MSC: 47A63 Linear operator inequalities 47B25 Linear symmetric and selfadjoint operators (unbounded) Keywords:convex inequalities; arithmetic mean; Jensen’s discrete inequality; selfadjoint operators × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] Dragomir S. S., Ionescu N. M.: On some inequalities for convex-dominated functions. Anal. Num. Théor. Approx. 19 (1990), 21-28. · Zbl 0733.26010 [2] Dragomir S. S.: An improvement of Jensen’s inequality. Bull. Math. Soc. Sci. Math. Roumaniè 34 (1990), 291-296. · Zbl 0753.26010 [3] Dragomir S. S.: An improvement of Jensen’s inequality. Math. Bilten (Skopje) 15 (1991), 35-37. · Zbl 0791.26012 [4] Dragomir S. S., Ionescu N. M.: A new refinement of Jensen’s inequality. Anal. Num. Théor. Approx. 20 (1991), 39-41. · Zbl 0758.26013 [5] Dragomir S. S.: Some refinements of Ky Fan’s inequality. J. Math. Anal. Appl. 163 (1992), 317-321. · Zbl 0768.26006 · doi:10.1016/0022-247X(92)90254-B [6] Dragomir S. S.: Some inequalities for convex functions. Macedonian Acad. Sci. Arts, Contributions 10 (1989), 25-28. · Zbl 0853.26011 [7] Dragomir S. S.: Some refinements of Jensen’s inequality. J. Math. Anal. Appl. 168 (1992), 518-522. · Zbl 0765.26007 · doi:10.1016/0022-247X(92)90177-F [8] Mond B.: An inequality for operators in a Hiìbert space. Pacific J. Math. 18 (1966), 161-163. · Zbl 0146.12504 · doi:10.2140/pjm.1966.18.161 [9] Mond B., Shisha O.: A difference inequality for operators in Hilbert space. Blanch Anriiversary Volume (B. Mond, editor), Aerospace Res. Lab., United States Air Force 1967, 269-275. · Zbl 0165.15101 [10] Mond B., Shisha O.: Difference and ratio inequalities in Hilbert space. Inequalities, Vol. II (O. Shisha, editor), Academic Press lnc., New York, 1970, 241-249. · Zbl 0217.45401 [11] Pečarić J. E., Dragomir S. S.: A refinement of Jensen’s inequality and applications. Studia Univ. Babes-Bolyai 34 (1989), 15-19. · Zbl 0687.26009 [12] Pečarić J. E., Dragomir S. S.: Some inequalities for quasi-linear functionals. Punime Mat. 4 (1989), 37-41. · Zbl 0731.26012 [13] Riesz F., Nagy B. Sz.: Functional Analysis. · Zbl 0070.10902 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.