{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,16]],"date-time":"2024-06-16T06:10:13Z","timestamp":1718518213737},"reference-count":8,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,2,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Sets of operators which have a given set of numbers in the numerical range are studied. We prove an interesting result which characterizes the set of operators that have 0 in the convex hull of its spectrum. Along the way we give a simpler proof of the well known Hilbebrandt\u2019s theorem.<\/jats:p>","DOI":"10.1515\/ms-2015-0134","type":"journal-article","created":{"date-parts":[[2016,5,3]],"date-time":"2016-05-03T08:42:23Z","timestamp":1462264943000},"page":"275-280","source":"Crossref","is-referenced-by-count":0,"title":["Operators with a given part of the numerical range"],"prefix":"10.1515","volume":"66","author":[{"given":"Janko","family":"Bra\u010di\u010d","sequence":"first","affiliation":[{"name":"University of Ljubljana IMFM, Jadranska ul. 19 SI\u20131000 Ljubljana SLOVENIA"}]},{"given":"Cristina","family":"Diogo","sequence":"additional","affiliation":[{"name":"Instituto Universit\u00e1rio de Lisboa (ISCTE-IUL) Avenida das For\u00e7as Armadas P\u20131649-026 Lisboa PORTUGAL and Center for Mathematical Analysis, Geometry, and Dynamical Systems Departamento de Matem\u00e1tica Instituto Superior T\u00e9cnico P\u20131049-001 Lisboa PORTUGAL"}]}],"member":"374","published-online":{"date-parts":[[2016,4,30]]},"reference":[{"key":"2021062123241647834_j_ms-2015-0134_ref_001_w2aab3b8d495b1b7b1ab2b2b1Aa","doi-asserted-by":"crossref","unstructured":"Gustafson K. E.\u2014Rao D. K. M.: Numerical Range, Springer-Verlag, New York, 1997.","DOI":"10.1007\/978-1-4613-8498-4"},{"key":"2021062123241647834_j_ms-2015-0134_ref_002_w2aab3b8d495b1b7b1ab2b2b2Aa","doi-asserted-by":"crossref","unstructured":"Halmos P. R.: A Hilbert Space Problem Book, Springer-Verlag, New-York, 1982.","DOI":"10.1007\/978-1-4684-9330-6"},{"key":"2021062123241647834_j_ms-2015-0134_ref_003_w2aab3b8d495b1b7b1ab2b2b3Aa","doi-asserted-by":"crossref","unstructured":"Hildebrandt S.: \u00fcber den Numerischen Wertebereich eines Operators, Math. Ann. 163 (1966), 230\u2013247.","DOI":"10.1007\/BF02052287"},{"key":"2021062123241647834_j_ms-2015-0134_ref_004_w2aab3b8d495b1b7b1ab2b2b4Aa","doi-asserted-by":"crossref","unstructured":"Laursen K.B.\u2014Neumann M.N.: An Introduction to Local Spectral Theory . London Math. Soc. Monogr. 20, Clarendon Press, Oxford, 2000.","DOI":"10.1093\/oso\/9780198523819.001.0001"},{"key":"2021062123241647834_j_ms-2015-0134_ref_005_w2aab3b8d495b1b7b1ab2b2b5Aa","unstructured":"M\u00fcller V.: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras (2nd ed.). Oper. Theory Adv. Appl. 139, Birkh\u00e4user, Basel, 2007."},{"key":"2021062123241647834_j_ms-2015-0134_ref_006_w2aab3b8d495b1b7b1ab2b2b6Aa","doi-asserted-by":"crossref","unstructured":"Murphy G.J.\u2014West T.T.: Spectral radius formulae, Proc. Edinb. Math. Soc. (2) 22 (1979), 271\u2013275.","DOI":"10.1017\/S0013091500016448"},{"key":"2021062123241647834_j_ms-2015-0134_ref_007_w2aab3b8d495b1b7b1ab2b2b7Aa","doi-asserted-by":"crossref","unstructured":"Paul K.\u2014Das G.: Cosine of an angle and center of mass of an operator, Math. Slovaca 62 (2012), 109\u2013122.","DOI":"10.2478\/s12175-011-0076-4"},{"key":"2021062123241647834_j_ms-2015-0134_ref_008_w2aab3b8d495b1b7b1ab2b2b8Aa","doi-asserted-by":"crossref","unstructured":"Williams J.: Similarity and the numerical range, J. Math. Anal. App. 26 (1969), 307\u2013314.","DOI":"10.1016\/0022-247X(69)90154-1"}],"container-title":["Mathematica Slovaca"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ms-2015-0134\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ms-2015-0134\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,16]],"date-time":"2024-06-16T05:13:35Z","timestamp":1718514815000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ms-2015-0134\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,1]]},"references-count":8,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,4,26]]},"published-print":{"date-parts":[[2016,2,1]]}},"alternative-id":["10.1515\/ms-2015-0134"],"URL":"https:\/\/doi.org\/10.1515\/ms-2015-0134","relation":{},"ISSN":["1337-2211","0139-9918"],"issn-type":[{"value":"1337-2211","type":"electronic"},{"value":"0139-9918","type":"print"}],"subject":[],"published":{"date-parts":[[2016,2,1]]}}}