On the numerical range of some block matrices with scalar diagonal blocks

2019/11/01 by Geryba, Titas, Spitkovsky, Ilya M. · 2 citations
#15A60 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1911.00273

Abstract

Several new verifiable conditions are established for block matrices with scalar diagonal blocks to have the numerical range equal the convex hull of at most k ellipses where k by k is the size of the smaller diagonal block. For k = 2, these conditions are also necessary, provided that the ellipses are co-centered.

Cited by

• On the ellipticity of the higher rank numerical range
• Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case

Related

• On some 4-by-4 matrices with bi-elliptical numerical ranges
• A note on the essential numerical range of block diagonal operators
• Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case
• Numerical range and positive block matrices
• The possible shapes of numerical ranges