--- res: bibo_abstract: - Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Andreas foaf_name: Deuchert, Andreas foaf_surname: Deuchert orcid: 0000-0003-3146-6746 - foaf_Person: foaf_givenName: Christian foaf_name: Hainzl, Christian foaf_surname: Hainzl - foaf_Person: foaf_givenName: Robert foaf_name: Seiringer, Robert foaf_surname: Seiringer foaf_workInfoHomepage: http://www.librecat.org/personId=4AFD0470-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-6781-0521 bibo_doi: 10.1007/s11005-015-0787-5 bibo_issue: '10' bibo_volume: 105 dct_date: 2015^xs_gYear dct_language: eng dct_publisher: Springer@ dct_title: Note on a family of monotone quantum relative entropies@ ...