{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T13:12:56Z","timestamp":1778332376207,"version":"3.51.4"},"reference-count":23,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Approximation Theory"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.jat.2026.106286","type":"journal-article","created":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T16:13:21Z","timestamp":1771431201000},"page":"106286","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Convergence of random products of countably infinitely many projections"],"prefix":"10.1016","volume":"317","author":[{"given":"Rasoul","family":"Eskandari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Sal","family":"Moslehian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.jat.2026.106286_b1","first-page":"239","article-title":"Convergence of random products of contractions in Hilbert space","volume":"26","author":"Amemiya","year":"1965","journal-title":"Acfa Sci. Math. (Szeged)"},{"issue":"3","key":"10.1016\/j.jat.2026.106286_b2","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1090\/S1061-0022-2012-01202-1","article-title":"The rate of convergence in the method of alternating projections,translated from algebra i analiz 23 (2011), no. 3, 1-30","volume":"23","author":"Badea","year":"2012","journal-title":"St. Petersburg Math. J."},{"key":"10.1016\/j.jat.2026.106286_b3","series-title":"Recent Developments in Optimization Theory and Nonlinear Analysis (Jerusalem, 1995)","first-page":"1","article-title":"The method of cyclic projections for closed convex sets in Hilbert space","volume":"vol. 204","author":"Bauschke","year":"1997"},{"key":"10.1016\/j.jat.2026.106286_b4","series-title":"Approximation Theory, Wavelets and Applications (Maratea, 1994)","first-page":"107","article-title":"The angle between subspaces of a Hilbert space","volume":"vol. 454","author":"Deutsch","year":"1995"},{"key":"10.1016\/j.jat.2026.106286_b5","series-title":"CMS Books in Mathematics\/Ouvrages de Math\u00e9matiques de la SMC","article-title":"Best approximation in inner product spaces","author":"Deutsch","year":"2001"},{"issue":"1","key":"10.1016\/j.jat.2026.106286_b6","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0022-247X(91)90385-D","article-title":"On the unrestricted iteration of projections in Hilbert space","volume":"156","author":"Dye","year":"1991","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.jat.2026.106286_b7","series-title":"Unrestricted iterations of nonexpansive mappings in Hilbert space, nonlinear anal","first-page":"199","author":"Dye","year":"1992"},{"issue":"2","key":"10.1016\/j.jat.2026.106286_b8","first-page":"96","article-title":"The product of projection operators","volume":"23","author":"Halperin","year":"1962","journal-title":"Acta Sci. Math"},{"issue":"2","key":"10.1016\/j.jat.2026.106286_b9","doi-asserted-by":"crossref","first-page":"175","DOI":"10.4064\/sm223-2-4","article-title":"A product of three projections","volume":"223","author":"Kopeck\u00e1","year":"2014","journal-title":"Studia Math."},{"issue":"1","key":"10.1016\/j.jat.2026.106286_b10","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s11856-017-1480-4","article-title":"Strange products of projections","volume":"219","author":"Kopeck\u00e1","year":"2017","journal-title":"Israel J. Math."},{"issue":"3","key":"10.1016\/j.jat.2026.106286_b11","first-page":"379","article-title":"A note on the von Neumann alternating projections algorithm","volume":"5","author":"Kopeck\u00e1","year":"2004","journal-title":"J. Nonlinear Convex Anal."},{"issue":"3","key":"10.1016\/j.jat.2026.106286_b12","first-page":"455","article-title":"Another note on the von Neumann alternating projections algorithm","volume":"11","author":"Kopeck\u00e1","year":"2010","journal-title":"J. Nonlinear Convex Anal."},{"issue":"1","key":"10.1016\/j.jat.2026.106286_b13","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1007\/s10957-022-02028-9","article-title":"Strong convergence of alternating projections","volume":"194","author":"Melo","year":"2022","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.jat.2026.106286_b14","series-title":"C\u2217-Algebras and Operator Theory","author":"Murphy","year":"1990"},{"key":"10.1016\/j.jat.2026.106286_b15","doi-asserted-by":"crossref","first-page":"401","DOI":"10.2307\/1969463","article-title":"On rings of operators. Reduction theory","volume":"50","author":"von Neumann","year":"1949","journal-title":"Ann. Math."},{"key":"10.1016\/j.jat.2026.106286_b16","unstructured":"Paszkiewicz, A., The Amemiya\u2013Ando conjecture falls. arXiv:1203.3354."},{"key":"10.1016\/j.jat.2026.106286_b17","doi-asserted-by":"crossref","first-page":"271","DOI":"10.21136\/CMJ.1960.100409","article-title":"\u00dcber ein konvergenzprinzip im Hilbertschen raum","volume":"10","author":"Pr\u00e1ger","year":"1960","journal-title":"Czechoslovak Math. J."},{"issue":"2","key":"10.1016\/j.jat.2026.106286_b18","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/j.jmaa.2011.02.030","article-title":"Convergence of non-cyclic infinite products of operators","volume":"380","author":"Pustylnik","year":"2011","journal-title":"J. Math. Anal. Appl."},{"issue":"5","key":"10.1016\/j.jat.2026.106286_b19","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1016\/j.jat.2012.01.001","article-title":"Convergence of non-periodic infinite products of orthogonal projections and nonexpansive operators in Hilbert space","volume":"164","author":"Pustylnik","year":"2012","journal-title":"J. Approx. Theory"},{"key":"10.1016\/j.jat.2026.106286_b20","first-page":"423","article-title":"Inner inclination of subspaces and infinite products of orthogonal projections","volume":"14","author":"Pustylnik","year":"2013","journal-title":"J. Nonlinear Convex Anal."},{"key":"10.1016\/j.jat.2026.106286_b21","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1080\/00036819508840393","article-title":"Strong convergence of infinite products of orthogonal projections in Hilbert space","volume":"59","author":"Sakai","year":"1995","journal-title":"Appl. Anal."},{"issue":"1","key":"10.1016\/j.jat.2026.106286_b22","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s10957-024-02504-4","article-title":"Most iterations of projections converge","volume":"203","author":"Thimm","year":"2024","journal-title":"J. Optim. Theory Appl."},{"key":"10.1016\/j.jat.2026.106286_b23","first-page":"81","article-title":"On a meager full measure subset of N-ary sequences","volume":"6","author":"Thimm","year":"2024","journal-title":"Appl. Set-Valued Anal. Optim."}],"container-title":["Journal of Approximation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021904526000031?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021904526000031?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T13:04:16Z","timestamp":1778331856000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021904526000031"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":23,"alternative-id":["S0021904526000031"],"URL":"https:\/\/doi.org\/10.1016\/j.jat.2026.106286","relation":{},"ISSN":["0021-9045"],"issn-type":[{"value":"0021-9045","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Convergence of random products of countably infinitely many projections","name":"articletitle","label":"Article Title"},{"value":"Journal of Approximation Theory","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jat.2026.106286","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"106286"}}