A projection P 0 on a complex Banach space is generalized 3circular if its linear combination with two projections P 1 and P 2 having coefficients λ 1 and λ 2 , respectively, is a surjective isometry, where λ 1 and λ 2 are distinct unit modulus complex numbers different from 1 and P 0 ⊕ P 1 ⊕ P 2 = I. Such projections are always contractive. In this paper, we prove structure theorems for generalized 3-circular projections acting on the spaces of all n × n symmetric and skew-symmetric matrices over C when these spaces are equipped with unitary congruence invariant norms.
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