## Banach Journal of Mathematical Analysis

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

Abdullah Bin Abu Baker

#### Abstract

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.

#### Article information

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

Dates
Accepted: 17 August 2015
First available in Project Euclid: 13 May 2016

https://projecteuclid.org/euclid.bjma/1463153910

Digital Object Identifier
doi:10.1215/17358787-3599609

Mathematical Reviews number (MathSciNet)
MR3504179

Zentralblatt MATH identifier
1356.46010

#### Citation

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. https://projecteuclid.org/euclid.bjma/1463153910

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