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1987•Linear and Multilinear AlgebraRequires access

Linear operators preserving the higher numerical radius of matrices

Chi-Kwong Li

Open publisher page 21 citations

Abstract

A linear operator T on a matrix space is said to be unital if T(I) = I. In this note we characterize the unital lineart operators on matrix spaces that preserve the k-numerical radius. Using the results obtained we easily determine the structure of all linear operators on the space of n × n complex matrices that preserve the k-numerical range. This completes the work of Pierce and Watking, who obtained the results for the cases when n ≠ n2k.

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What this paper is about

A linear operator T on a matrix space is said to be unital if T(I) = I. In this note we characterize the unital lineart operators on matrix spaces that preserve the k-numerical radius. Using the results obtained we easily determine the structure of all linear operators on the space of n × n complex matrices that preserve the k-numerical range. This completes the work of Pierce and Watking, who obtained the results for the cases when n ≠ n2k.

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Available abstract

A linear operator T on a matrix space is said to be unital if T(I) = I. In this note we characterize the unital lineart operators on matrix spaces that preserve the k-numerical radius. Using the results obtained we easily determine the structure of all linear operators on the space of n × n complex matrices that preserve the k-numerical range. This completes the work of Pierce and Watking, who obtained the results for the cases when n ≠ n2k.

Key concepts: Mathematics, Numerical range, Linear operators, Operator matrix, Matrix (chemical analysis), Linear map, Spectral radius, RADIUS

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