Banach Journal of Mathematical Analysis

Generalized 3-circular projections for unitary congruence invariant norms

Abdullah Bin Abu Baker

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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 P0P1P2=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.

Article information

Banach J. Math. Anal., Volume 10, Number 3 (2016), 451-465.

Received: 16 March 2015
Accepted: 17 August 2015
First available in Project Euclid: 13 May 2016

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Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]

spectral theorem isometry generalized 3-circular projection unitary congruence invariant norm


Abu Baker, Abdullah Bin. Generalized $3$ -circular projections for unitary congruence invariant norms. Banach J. Math. Anal. 10 (2016), no. 3, 451--465. doi:10.1215/17358787-3599609.

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