Analytic equivalence and similarity of operators |
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Authors: | Benoî t Pruvost |
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Affiliation: | (1) UFR de Mathématiques, Bât. M2, Université de Lille 1, Cité Scientifique, F-59655 Villeneuve d'Ascq, France |
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Abstract: | The analytic equivalence of two operators is a generalization of similarity. We prove that under some conditions the analytic equivalence between two Hilbert space operatorsT andR implies the similarity of their restrictions on generalized ranges. We also prove that, in certain cases, the similarity ofT to a contraction implies that ofR. An improvement of a well-known criterion of similarity to an isometry due to Sz.-Nagy is given and an extension of a result of Apostol is obtained. |
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Keywords: | 47A10 47A11 47A56 |
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