Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

G. Soares; N. Bebiano; R. Lemos

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Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

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arxiv 2508.12039 v1 pith:YEM7BR34 submitted 2025-08-16 math.FA

N. Bebiano , R. Lemos , G. Soares This is my paper

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abstract

In this paper, we investigate the Krein space numerical range of $2$-by-$2$ block matrices, with diagonal blocks as scalar multiples of the identity. For these matrices, we specifically investigate the cases when the respective boundary generating curves consist of hyperbolas. This provides a unified approach to derive established and new results concerning the numerical range hyperbolic shape.

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