Aluthge Transforms of Complex Symmetric Operators

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Some new classes of complex symmetric operators (2009, background): “ order 2 (i.e. T2 = 0), then T is a complex symmetric operator. A direct proof of the second portion of Corollary 4, involving the explicit construction of the associated conjugation, can be found in [5]. Yet another basic class of operators that happen to be complex symmetric are the rank-one opera”
On local spectral properties of complex symmetric operators (2011, background): “Since T̃ (k) is hyponormal and complex symmetric by [10], it follows that T̃ (k) is normal by [10].”
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].”