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S-spectrum and numerical range of a quaternionic operator
Luís Carvalho, Cristina Diogo, Sérgio Mendes
We study the numerical range of bounded linear operators on quaternionic Hilbert spaces and its relation with the S-spectrum. The class of complex operators on quaternionic Hilbert…
On the convexity of the quaternionic essential numerical range
Luís Carvalho, Cristina Diogo, Sérgio Mendes +1
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 on…
The star-center of the quaternionic numerical range
Luís Carvalho, Cristina Diogo, Sérgio Mendes
In this paper we prove that the quaternionic numerical range is always star-shaped and its star-center is given by the equivalence classes of the star-center of the bild. We determ…
On the convexity and circularity of the numerical range of nilpotent quaternionic matrices
Luís Carvalho, Cristina Diogo, Sérgio Mendes
We provide a sufficient condition for the numerical range of a nilpotent matrix N to be circular in terms of the existence of cycles in an undirected graph associated with N. We pr…
A bridge between quaternionic and complex numerical ranges
Luís Carvalho, Cristina Diogo, Sérgio Mendes
We obtain a sufficient condition for the convexity of quaternionic numerical range for complex matrices in terms of its complex numerical range. It is also shown that the Bild coin…