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On the convexity of the quaternionic essential numerical range
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AbstractThe 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.
Cambridge University Press (CUP)
Title: On the convexity of the quaternionic essential numerical range
Description:
AbstractThe 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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