Complex symmetric partial isometries
By Stephan Ramon Garcia, W. Wogen. 2009
141 citations recorded by the source corpus.
An operator T∈B(H) is complex symmetric if there exists a conjugate-linear, isometric involution C:H→H so that T=CT∗C. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension ⩽4 is complex symmetric.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/485cc906d558ee53411b5bb28fd88c9af4b3e304
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In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Complex symmetric weighted composition operators on H2(D) (2014, background): “We refer the reader to [13,15–18], and [26] for more details, including historical comments and references.”
- Recent Progress on Truncated Toeplitz Operators (2011, background): “In particular, Theorem 12 says each truncated Toeplitz operator is a complex symmetric operator, a class of Hilbert space operators which has undergone much recent study [24, 35, 45–50, 54, 55, 61, 63, 71, 72, 74, 103–107].”
- Some new classes of complex symmetric operators (2009, background): “We refer the reader to [10] for the resolution of this problem.”
- Which Weighted Composition Operators are Complex Symmetric (2011, unknown): “Wogen, in various combinations, in [7–10].”
- On local spectral properties of complex symmetric operators (2011, background): “This class includes all normal operators, Hankel operators, compressed Toeplitz operators, and the Volterra integration operator, and there are a lot of consequences and applications concerning complex symmetric operators (see [10–16,26], etc.”