{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T06:58:12Z","timestamp":1772521092556,"version":"3.50.1"},"reference-count":17,"publisher":"Canadian Mathematical Society","issue":"1","license":[{"start":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T00:00:00Z","timestamp":1587081600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Can. Math. Bull."],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For an inner function <jats:italic>u<\/jats:italic>, we discuss the dual operator for the compressed shift <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0008439520000260_inline1.png\"\/><jats:tex-math>$P_u S|_{{\\mathcal {K}}_u}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, where <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0008439520000260_inline2.png\"\/><jats:tex-math>${\\mathcal {K}}_u$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is the model space for <jats:italic>u<\/jats:italic>. We describe the unitary equivalence\/similarity classes for these duals as well as their invariant subspaces.<\/jats:p>","DOI":"10.4153\/s0008439520000260","type":"journal-article","created":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T09:43:05Z","timestamp":1587116585000},"page":"98-111","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":7,"title":["The Dual of the Compressed Shift"],"prefix":"10.4153","volume":"64","author":[{"given":"M. C.","family":"C\u00e2mara","sequence":"first","affiliation":[]},{"given":"W. 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Spaces"},{"key":"S0008439520000260_r9","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1215\/17358787-2018-0030","volume":"13","author":"Ding","year":"2019","journal-title":"Banach J. Math. Anal"},{"key":"S0008439520000260_r16","doi-asserted-by":"crossref","first-page":"2495","DOI":"10.1090\/S0002-9947-02-02954-9","article-title":"Algebraic and spectral properties of dual Toeplitz operators","volume":"354","author":"Stroethoff","year":"2002","journal-title":"Trans. Amer. Math. Soc."},{"key":"S0008439520000260_r17","unstructured":"[17] Li, Y. S. Y. and Ding, X. , The commutatant and invariant subspaces for a class of dual truncated Toeplitz operators. Preprint."},{"key":"S0008439520000260_r8","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s43034-019-00002-7","article-title":"A theorem of Brown-Halmos type for dual truncated Toeplitz operators","volume":"11","author":"Ding","year":"2020","journal-title":"Ann. Funct. 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