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math.FA2022
A note on the essential numerical range of block diagonal operators
Luís Carvalho, Cristina Diogo, Sérgio Mendes +1
In this note we characterize the essential numerical range of a block diagonal o\-pe\-ra\-tor in terms of the numerical ranges of its components.…
math.FA2022
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…
math.FA2022
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…