Generalized $3$ -circular projections for unitary congruence invariant norms

Abstract

A projection P0 on a complex Banach space is generalized 3- circular if its linear combination with two projections P1 and P2 having coefficients λ1 and λ2, respectively, is a surjective isometry, where λ1 and λ2 are distinct unit modulus complex numbers different from 1 and P0⊕P1⊕P2=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.