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arXiv · 2210.05520

On the convexity of the quaternionic essential numerical range

Luís Carvalho·Cristina Diogo·Sérgio Mendes·Helena Soares
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Abstract

The numerical range in the quaternionic setting is, in general, a non convex subset of the quaternions. The essential numerical range is a refinement of the numerical range that only keeps the elements that have, in a certain sense, infinite multiplicity. We prove that the essential numerical range of a bounded linear operator on a quaternionic Hilbert space is convex. A quaternionic analogue of Lancaster theorem, relating the closure of the numerical range and its essential numerical range, is also provided.

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Luís Carvalho, Cristina Diogo, Sérgio Mendes, Helena Soares. 2022-10-11. On the convexity of the quaternionic essential numerical range. https://arxiv.org/abs/2210.05520

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