Abstract.
We consider isometric operators with finite defect numbers that are unitarily equivalent to their Möbius transformations. A functional characterization of such isometries is given in terms of their characteristic operator-functions. We show that any such isometry admits a contractive extension that is also unitarily equivalent to its Möbius transformation and a unitary extension in a larger space that has the same property. Examples of automorphic invariant operators are considered.
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Communicated by Leiba Rodman.
The author is very thankful to Mark Nudelman and David Grow for useful discussions and constructive comments. The author also wants to express his gratitude to the anonymous referee for useful suggestions and pointing out some references that are relevant to the topics presented in this article.
Submitted: January 15, 2008. Accepted: May 5, 2008.
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Bekker, M.B. Automorphic Invariant Isometric Operators. Complex Anal. Oper. Theory 3, 587 (2009). https://doi.org/10.1007/s11785-008-0076-8
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DOI: https://doi.org/10.1007/s11785-008-0076-8