{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:48:13Z","timestamp":1760233693265,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T00:00:00Z","timestamp":1613001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy\u2013Bunyakovsky\u2013Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr\u2019s inequality and Bergstr\u00f6m\u2019s inequality for operators. We present an inequality of the Cauchy\u2013Bunyakovsky\u2013Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Acz\u00e9l inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators.<\/jats:p>","DOI":"10.3390\/sym13020305","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T16:12:10Z","timestamp":1613146330000},"page":"305","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["About the Cauchy\u2013Bunyakovsky\u2013Schwarz Inequality for Hilbert Space Operators"],"prefix":"10.3390","volume":"13","author":[{"given":"Nicu\u015for","family":"Minculete","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Bra\u015fov, Iuliu Maniu Street, No. 50, 500091 Bra\u015fov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sunder, V.S. (2016). 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