Abstract
We show that the numerical and block numerical range of positive operators on Banach lattices have many properties that resemble the spectral properties of positive operators. In particular, we show that the (block) numerical radius is always contained in the closure of the (block) numerical range. Moreover, the (block) numerical range is symmetric with respect to the real axis. For irreducible operators on suitable \(L^p\)-spaces we prove a rotational symmetry for the (block) numerical range. In addition, we determine the numerical range and radius for some concrete operators.
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Acknowledgments
I am grateful to Karl-Heinz Förster for many valuable discussions and comments. In particular, I thank him for bringing the block numerical range in Banach spaces to my attention.
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Radl, A. The numerical range of positive operators on Banach lattices. Positivity 19, 603–623 (2015). https://doi.org/10.1007/s11117-014-0318-0
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DOI: https://doi.org/10.1007/s11117-014-0318-0