{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T01:09:49Z","timestamp":1778548189027,"version":"3.51.4"},"reference-count":8,"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"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Croatian Science Foundation","doi-asserted-by":"publisher","award":["IP-2022-10-5191"],"award-info":[{"award-number":["IP-2022-10-5191"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics Letters"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.aml.2026.109968","type":"journal-article","created":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T07:03:32Z","timestamp":1776495812000},"page":"109968","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Schatten norm estimates for Lyapunov gramians in operator scales"],"prefix":"10.1016","volume":"179","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3370-9353","authenticated-orcid":false,"given":"Luka","family":"Grubi\u0161i\u0107","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4034-5770","authenticated-orcid":false,"given":"Martin","family":"Lazar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-9788-792X","authenticated-orcid":false,"given":"Juan Ricardo","family":"Mu\u00f1oz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"5","key":"10.1016\/j.aml.2026.109968_b1","doi-asserted-by":"crossref","first-page":"4084","DOI":"10.1137\/120885310","article-title":"Finite-rank ADI iteration for operator Lyapunov equations","volume":"51","author":"Opmeer","year":"2013","journal-title":"SIAM J. Control Optim."},{"key":"10.1016\/j.aml.2026.109968_b2","doi-asserted-by":"crossref","DOI":"10.1016\/j.sysconle.2025.106308","article-title":"Pollution free eigenvalue bounds for the gramian operator","volume":"208","author":"Grubi\u0161i\u0107","year":"2026","journal-title":"Systems Control Lett."},{"key":"10.1016\/j.aml.2026.109968_b3","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.sysconle.2014.09.006","article-title":"On the eigenvalue decay of solutions to operator Lyapunov equations","volume":"73","author":"Grubi\u0161i\u0107","year":"2014","journal-title":"Systems Control Lett."},{"key":"10.1016\/j.aml.2026.109968_b4","series-title":"Trace Ideals and their Applications","volume":"vol. 120","author":"Simon","year":"2005"},{"key":"10.1016\/j.aml.2026.109968_b5","series-title":"Classics in Mathematics","article-title":"Perturbation Theory for Linear Operators","author":"Kato","year":"1995"},{"key":"10.1016\/j.aml.2026.109968_b6","series-title":"Observation and Control for Operator Semigroups","author":"Tucsnak","year":"2009"},{"key":"10.1016\/j.aml.2026.109968_b7","series-title":"Functional Analysis, Sobolev Spaces and Partial Differential Equations","author":"Brezis","year":"2011"},{"key":"10.1016\/j.aml.2026.109968_b8","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2024.111653","article-title":"Eigenvalue bounds for the gramian operator of the heat equation","volume":"164","author":"Lazar","year":"2024","journal-title":"Automatica"}],"container-title":["Applied Mathematics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965926000996?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965926000996?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T00:21:48Z","timestamp":1778545308000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893965926000996"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":8,"alternative-id":["S0893965926000996"],"URL":"https:\/\/doi.org\/10.1016\/j.aml.2026.109968","relation":{},"ISSN":["0893-9659"],"issn-type":[{"value":"0893-9659","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Schatten norm estimates for Lyapunov gramians in operator scales","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.aml.2026.109968","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"109968"}}