{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T07:43:04Z","timestamp":1774510984978,"version":"3.50.1"},"reference-count":8,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,6,5]],"date-time":"2011-06-05T00:00:00Z","timestamp":1307232000000},"content-version":"vor","delay-in-days":155,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2011,1]]},"abstract":"Let \u2112<\/jats:italic> be the space of complex\u2010valued functions f<\/jats:italic> on the set of vertices T<\/jats:italic> of an infinite tree rooted at o<\/jats:italic> such that the difference of the values of f<\/jats:italic> at neighboring vertices remains bounded throughout the tree, and let \u2112<\/jats:italic>w<\/jats:bold><\/jats:sub> be the set of functions f<\/jats:italic> \u2208 \u2112<\/jats:italic> such that |f<\/jats:italic>(v<\/jats:italic>) \u2212 f<\/jats:italic>(v<\/jats:italic>\u2212<\/jats:sup>)| = O<\/jats:italic>(|v<\/jats:italic>|\u22121<\/jats:sup>), where |v<\/jats:italic>| is the distance between o<\/jats:italic> and v<\/jats:italic> and v<\/jats:italic>\u2212<\/jats:sup> is the neighbor of v<\/jats:italic> closest to o<\/jats:italic>. In this paper, we characterize the bounded and the compact multiplication operators between \u2112<\/jats:italic> and \u2112<\/jats:italic>w<\/jats:bold><\/jats:sub> and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between \u2112<\/jats:italic>w<\/jats:bold><\/jats:sub> and the space L<\/jats:italic>\u221e<\/jats:italic><\/jats:sup> of bounded functions on T<\/jats:italic> and determine their operator norm and their essential norm. We establish that there are no isometries among the multiplication operators between these spaces.<\/jats:p>","DOI":"10.1155\/2011\/472495","type":"journal-article","created":{"date-parts":[[2011,6,5]],"date-time":"2011-06-05T19:34:24Z","timestamp":1307302464000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Multiplication Operators between Lipschitz\u2010Type Spaces on a Tree"],"prefix":"10.1155","volume":"2011","author":[{"given":"Robert F.","family":"Allen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Flavia","family":"Colonna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Glenn R.","family":"Easley","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,6,5]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02843992"},{"key":"e_1_2_7_2_2","series-title":"Monographs and Textbooks in Pure and Applied Mathematics","volume-title":"Operator Theory in Function Spaces","author":"Zhu K. H.","year":"1990"},{"key":"e_1_2_7_3_2","first-page":"203","volume-title":"Symposia Mathematica","author":"Cartier P.","year":"1972"},{"key":"e_1_2_7_4_2","first-page":"311","article-title":"Embeddings of trees in the hyperbolic disk","volume":"24","author":"Cohen J. M.","year":"1994","journal-title":"Complex Variables"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00020\u2010010\u20101824\u20105"},{"key":"e_1_2_7_6_2","unstructured":"AllenR. F. ColonnaF. andEasleyG. R. Multiplication operators on the weighted Lipschitz space of a tree to appear inThe Journal of Operator Theory."},{"key":"e_1_2_7_7_2","unstructured":"ColonnaF.andEasleyG. R. Multiplication operators between the Lipschitz space and the space of bounded functions on a tree to appear inMediterranean Journal of Mathematics."},{"key":"e_1_2_7_8_2","series-title":"Graduate Texts in Mathematics","volume-title":"A Course in Functional Analysis","author":"Conway J. B.","year":"1990"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/472495.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2011\/472495.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2011\/472495","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T13:49:34Z","timestamp":1718027374000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2011\/472495"}},"subtitle":[],"editor":[{"given":"Ingo","family":"Witt","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1155\/2011\/472495"],"URL":"https:\/\/doi.org\/10.1155\/2011\/472495","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1]]},"assertion":[{"value":"2010-12-04","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-03-16","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-06-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"472495"}}