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Generalized 3-circular projections for unitary congruence invariant norms. (English) Zbl 1356.46010

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

MSC:

46B04 Isometric theory of Banach spaces
47L05 Linear spaces of operators
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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References:

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