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We use this to define equivalences between two operators in that class by means of multipliers between the spaces where they act. Necessary and sufficient conditions for such an equivalence to be unitary or a similarity are established. The results are applied to Toeplitz and Hankel operators, truncated Toeplitz operators, and dual truncated Toeplitz operators.<\/jats:p>","DOI":"10.1007\/s43037-024-00349-7","type":"journal-article","created":{"date-parts":[[2024,5,5]],"date-time":"2024-05-05T11:01:22Z","timestamp":1714906882000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multipliers and equivalence of functions, spaces, and operators"],"prefix":"10.1007","volume":"18","author":[{"given":"M. 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