Conjugations of unitary operators, II

For a unitary operator U on a separable complex Hilbert space H , we describe the set C c ( U ) of all conjugations C (antilinear, isometric, and involutive maps) on H for which C U C = U . As this set might be empty, we also show that C c ( U ) ≠ ∅ if and only if U is unitarily equivalent to U ∗ ....

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Bibliographic Details
Published in:Analysis and mathematical physics 2024, Vol.14 (3), p.56, Article 56
Main Authors: Mashreghi, Javad, Ptak, Marek, Ross, William T.
Format: Article
Language:English
Subjects:
Analysis
Hilbert space
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Summary:For a unitary operator U on a separable complex Hilbert space H , we describe the set C c ( U ) of all conjugations C (antilinear, isometric, and involutive maps) on H for which C U C = U . As this set might be empty, we also show that C c ( U ) ≠ ∅ if and only if U is unitarily equivalent to U ∗ .
ISSN:1664-2368
1664-235X
1664-235X
DOI:10.1007/s13324-024-00920-3