## 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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