{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:30:34Z","timestamp":1776796234287,"version":"3.51.2"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"283","license":[{"start":{"date-parts":[[2014,1,11]],"date-time":"2014-01-11T00:00:00Z","timestamp":1389398400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, using some block-operator matrix techniques, we give necessary and sufficient conditions for the reverse order law to hold for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartSet 1 comma 2 comma 3 EndSet\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo fence=\"false\" stretchy=\"false\">{<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>3<\/mml:mn>\n                            <mml:mo fence=\"false\" stretchy=\"false\">}<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\{1,2,3\\}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    - and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartSet 1 comma 2 comma 4 EndSet\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo fence=\"false\" stretchy=\"false\">{<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>4<\/mml:mn>\n                            <mml:mo fence=\"false\" stretchy=\"false\">}<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\{1,2,4\\}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -inverses of bounded operators on Hilbert spaces. Furthermore, we present some new equivalents of the reverse order law for the Moore-Penrose inverse.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2013-02660-9","type":"journal-article","created":{"date-parts":[[2013,1,11]],"date-time":"2013-01-11T08:38:19Z","timestamp":1357893499000},"page":"1597-1607","source":"Crossref","is-referenced-by-count":15,"title":["New results on reverse order law for {1,2,3}- and {1,2,4}-inverses of bounded operators"],"prefix":"10.1090","volume":"82","author":[{"given":"Xiaoji","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuxia","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dragana","family":"Cvetkovi\u0107-Ili\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2013,1,11]]},"reference":[{"key":"1","series-title":"CMS Books in Mathematics\/Ouvrages de Math\\'{e}matiques de la SMC","isbn-type":"print","volume-title":"Generalized inverses","volume":"15","author":"Ben-Israel, Adi","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/0387002936","edition":"2"},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"1388","DOI":"10.1016\/j.laa.2010.11.022","article-title":"Reverse order laws in \ud835\udc36*-algebras","volume":"434","author":"Cvetkovi\u0107-Ili\u0107, Dragana S.","year":"2011","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"issue":"2","key":"3","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/j.aml.2010.09.005","article-title":"Reverse order laws for {1,3,4}-generalized inverses in \ud835\udc36*-algebras","volume":"24","author":"Cvetkovi\u0107-Ili\u0107, Dragana S.","year":"2011","journal-title":"Appl. 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