A projection on a complex Banach space is generalized - circular if its linear combination with two projections and having coefficients and , respectively, is a surjective isometry, where and are distinct unit modulus complex numbers different from and . Such projections are always contractive. In this paper, we prove structure theorems for generalized -circular projections acting on the spaces of all symmetric and skew-symmetric matrices over when these spaces are equipped with unitary congruence invariant norms.
"Generalized -circular projections for unitary congruence invariant norms." Banach J. Math. Anal. 10 (3) 451 - 465, July 2016. https://doi.org/10.1215/17358787-3599609